Description
F0X and F0Y are matrices over a common ring and respectively encode equations a subscheme/quotient module and its ambient scheme/module.
If SanityCheck is set to true, as is the default, then the algorithm will check that the relevant deformation equations are satisfied, and terminate with an error if this is not the case.
The parameters used in the perturbations may be specified by the options DefParamX and DefParamY.
For example, consider the cone over the rational normal curve of degree four and a fat point at the origin cut out by the square of the homogeneous maximal ideal. The following computes the nested Hilbert scheme of this pair:
i1 : R=QQ[x,y];
|
i2 : F0Y=basis(3,R);
1 4
o2 : Matrix R <-- R
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i3 : F0X=basis(2,R);
1 3
o3 : Matrix R <-- R
|
i4 : D=nestedHilbertScheme(F0X,F0Y,Verbose=>4);
Calculating first order relations
Calculating standard expressions for obstructions
Starting lifting
Order 2
Lifting family for X
Calculating tangent cone for obstructions
Calculating residual terms
Lifting Family
Calculating Obstruction Equations
Lifting Relations and Coefficients
Lifting family for Y
Calculating tangent cone for obstructions
Calculating residual terms
Lifting Family
Calculating Obstruction Equations
Lifting Relations and Coefficients
Calculating tangent cone for new obstructions
Calculating joint residual terms
Calculating Joint Obstruction Equations
Changing Families
Changing Relations
Lifting Submodule Relation
Correcting Coefficients
Doing Sanity Check
Checking polynomial lifting
Order 3
Lifting family for X
Calculating tangent cone for obstructions
Calculating residual terms
Lifting Family
Calculating Obstruction Equations
Lifting Relations and Coefficients
Lifting family for Y
Calculating tangent cone for obstructions
Calculating residual terms
Lifting Family
Calculating Obstruction Equations
Lifting Relations and Coefficients
Calculating tangent cone for new obstructions
Calculating joint residual terms
Calculating Joint Obstruction Equations
Changing Families
Changing Relations
Lifting Submodule Relation
Correcting Coefficients
Doing Sanity Check
Checking polynomial lifting
Solution is polynomial
|
i5 : transpose (families D)_0
o5 = {-2} | t_2t_3-t_3^2-t_1t_4+t_1t_5+yt_1+xt_2+x2 |
{-2} | t_3t_4-t_1t_6+yt_3+xt_4+xy |
{-2} | -t_4^2+t_4t_5+t_2t_6-t_3t_6+yt_5+xt_6+y2 |
3 1
o5 : Matrix (R[t ..t ]) <-- (R[t ..t ])
1 18 1 18
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i6 : transpose (families D)_1
o6 = {-3} | t_9t_11t_13-t_11^2t_13-t_8t_12t_13+t_10t_12t_13-t_9t_13^2+t
{-3} | t_11t_12t_13-t_12t_13^2-t_10t_12t_14-t_8t_13t_15+t_10t_13t_
{-3} | -t_12^2t_13+t_12t_13t_14+t_10t_12t_15+t_9t_13t_15-t_11t_13t
{-3} | t_12^2t_14-t_12t_14^2-t_11t_12t_15+t_12t_13t_15-t_9t_14t_15
------------------------------------------------------------------------
_11t_13^2-t_9t_10t_14+t_10t_11t_14+t_7t_12t_14+t_8t_13t_14-t_10t_13t_14-
15+t_7t_14t_15+t_10t_12t_16-t_7t_15t_16+t_8t_10t_18-t_10^2t_18-t_7t_11t_
_15-t_7t_15^2-t_10t_12t_17+t_7t_15t_17-t_9t_10t_18+t_10t_11t_18+t_7t_12t
+t_11t_14t_15+t_8t_15^2-t_10t_15^2-t_12^2t_16+t_12t_14t_16+t_9t_15t_16-t
------------------------------------------------------------------------
t_7t_14^2+t_8t_10t_15-t_10^2t_15-t_7t_11t_15+t_7t_13t_15+t_9t_10t
18+t_7t_13t_18+yt_10t_12+xt_11t_12+yt_11t_13-yt_13^2-yt_10t_14-yt
_18-t_7t_14t_18-xt_12^2+xt_12t_14+yt_13t_14+xt_9t_15+yt_10t_15-xt
_11t_15t_16+t_11t_12t_17-t_12t_13t_17-t_8t_15t_17+t_10t_15t_17+t_
------------------------------------------------------------------------
_16-t_10t_11t_16-t_7t_12t_16+t_7t_14t_16-t_8t_10t_17+t_10^2t_17+t_7t_11t
_7t_15-xt_8t_15+xt_10t_15+yt_10t_16-xt_7t_18+y2t_10+xyt_11+x2t_12+x2y
_11t_15+xt_13t_15-yt_10t_17-yt_7t_18-xt_10t_18+y2t_13+xyt_14+x2t_15+xy2
9t_11t_18-t_11^2t_18-t_8t_12t_18+t_10t_12t_18-t_9t_13t_18+t_11t_13t_18+t
------------------------------------------------------------------------
_17-t_7t_13t_17+yt_9t_10+xt_9t_11-yt_10t_11-xt_11^2-yt_7t_12-xt_8t_12+xt
_8t_14t_18-t_10t_14t_18-yt_12^2+yt_12t_14-yt_14^2+yt_9t_15-2yt_11t_15-xt
------------------------------------------------------------------------
_10t_12+yt_8t_13-yt_10t_13+xt_11t_13-xt_13^2+xt_8t_14-2xt_10t_14-xt_7t_
_12t_15+yt_13t_15-xt_14t_15+yt_14t_16+xt_15t_16+yt_11t_17+xt_12t_17-yt_
------------------------------------------------------------------------
15+yt_7t_16+xt_10t_16+xt_7t_17+y2t_7+xyt_8+x2t_9+x3 |
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13t_17+yt_8t_18+xt_9t_18-yt_10t_18-xt_13t_18+y2t_16+xyt_17+x2t_18+y3 |
4 1
o6 : Matrix (R[t ..t ]) <-- (R[t ..t ])
1 18 1 18
|
i7 : obstructions D
o7 = | 0
| 0
| 0
| 0
| t_1t_2+t_1t_3-t_5t_7-t_3t_8-t_1t_9+t_9t_10-t_10t_11-t_7t_
| t_2^2-t_2t_3+t_3^2+2t_1t_4-t_1t_5-t_6t_7-t_4t_8-t_2t_9+t_
| t_3^2+t_1t_4-t_5t_10-t_3t_11-t_1t_12+t_10t_12+t_11t_13-t_
| t_2t_4+t_1t_6-t_6t_10-t_4t_11-t_2t_12+t_11t_12-t_8t_15+t_
| t_3t_5+t_1t_6-t_5t_13-t_3t_14+t_13t_14-t_1t_15+t_10t_15-t
| t_4^2+t_3t_6-t_12^2-t_6t_13-t_4t_14+t_12t_14-t_2t_15+t_9t
| t_4^2-t_4t_5+t_5^2-t_2t_6+2t_3t_6-t_12^2+t_12t_14-t_14^2+
| t_4t_6+t_5t_6-t_12t_15-t_14t_15-t_6t_16+t_15t_16-t_4t_17+
------------------------------------------------------------------------
12+t_8t_13-t_10t_13+t_7t_16
9t_11-t_11^2-t_8t_12+t_10t_12+t_11t_13-t_13^2+t_8t_14-2t_10t_14-t_7t_15+
13^2-t_10t_14-t_7t_15+t_10t_16
10t_15-t_7t_18
_10t_17-t_7t_18
_15-t_11t_15+t_13t_15-t_10t_18
t_9t_15-2t_11t_15+t_13t_15-t_5t_16+t_14t_16-t_3t_17+t_11t_17-t_13t_17-t_
t_12t_17-t_2t_18+t_9t_18-t_13t_18
------------------------------------------------------------------------
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t_10t_16+t_7t_17 |
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1t_18+t_8t_18-t_10t_18 |
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12 1
o7 : Matrix (R[t ..t ]) <-- (R[t ..t ])
1 18 1 18
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If Projective is set to true then only degree zero deformations are considered; under favorable circumstances this will give the nested Hilbert/Quot scheme of the associated projective schemes or coherent sheaves.
For instance, consider the nested Hilbert scheme of a line on a singular cubic surface:
i8 : R=QQ[x_0..x_3];
warning: clearing value of symbol x to allow access to subscripted variables based on it
: debug with expression debug 9868 or with command line option --debug 9868
|
i9 : F0Y=gens ideal {x_1*x_2*x_3-x_0^3};
1 1
o9 : Matrix R <-- R
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i10 : F0X=gens ideal {x_1,x_0};
1 2
o10 : Matrix R <-- R
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i11 : D=nestedHilbertScheme(F0X,F0Y,Verbose=>4,Projective=>true);
Calculating first order relations
Calculating standard expressions for obstructions
Starting lifting
Order 2
Lifting family for X
Calculating tangent cone for obstructions
Calculating residual terms
Lifting Family
Calculating Obstruction Equations
Lifting Relations and Coefficients
Lifting family for Y
Calculating tangent cone for new obstructions
Calculating joint residual terms
Calculating Joint Obstruction Equations
Changing Families
Changing Relations
Lifting Submodule Relation
Correcting Coefficients
Doing Sanity Check
Checking polynomial lifting
Solution is polynomial
|
i12 : transpose (families D)_0
o12 = {-1} | x_0t_16+x_1t_17+x_2t_18+x_3t_19+x_1 |
{-1} | x_2t_14+x_3t_15+x_0 |
2 1
o12 : Matrix (R[t ..t ]) <-- (R[t ..t ])
1 19 1 19
|
i13 : transpose (families D)_1
o13 = {-3} | x_0x_2^2t_7t_14+x_0x_2x_3t_8t_14+x_1^2x_2t_9t_14+x_1x_2^2t_10t_
-----------------------------------------------------------------------
14+x_1x_2x_3t_11t_14+x_2^3t_12t_14+x_2x_3^2t_13t_14+x_0x_2^2t_14^2+x_0x
-----------------------------------------------------------------------
_2x_3t_7t_15+x_0x_3^2t_8t_15+x_1^2x_3t_9t_15+x_1x_2x_3t_10t_15+x_1x_3^
-----------------------------------------------------------------------
2t_11t_15+x_2^2x_3t_12t_15+x_3^3t_13t_15+2x_0x_2x_3t_14t_15+x_0x_3^2t_
-----------------------------------------------------------------------
15^2+x_0x_1^2t_1t_16+x_0x_1x_2t_2t_16+x_0x_1x_3t_3t_16+x_0x_2^2t_4t_16+
-----------------------------------------------------------------------
x_0x_3^2t_5t_16+x_0^3t_6t_16+x_1^3t_1t_17+x_1^2x_2t_2t_17+x_1^2x_3t_3t_
-----------------------------------------------------------------------
17+x_1x_2^2t_4t_17+x_1x_3^2t_5t_17+x_0^2x_1t_6t_17+x_1^2x_2t_1t_18+x_1x
-----------------------------------------------------------------------
_2^2t_2t_18+x_1x_2x_3t_3t_18+x_2^3t_4t_18+x_2x_3^2t_5t_18+x_0^2x_2t_6t_
-----------------------------------------------------------------------
18+x_1^2x_3t_1t_19+x_1x_2x_3t_2t_19+x_1x_3^2t_3t_19+x_2^2x_3t_4t_19+x_3
-----------------------------------------------------------------------
^3t_5t_19+x_0^2x_3t_6t_19+x_1^3t_1+x_1^2x_2t_2+x_1^2x_3t_3+x_1x_2^2t_4+
-----------------------------------------------------------------------
x_1x_3^2t_5+x_0^2x_1t_6+x_0^2x_2t_7+x_0^2x_3t_8+x_0x_1^2t_9+x_0x_1x_2t_
-----------------------------------------------------------------------
10+x_0x_1x_3t_11+x_0x_2^2t_12+x_0x_3^2t_13+x_0x_2x_3t_16+x_1x_2x_3t_17+
-----------------------------------------------------------------------
x_2^2x_3t_18+x_2x_3^2t_19-x_0^3+x_1x_2x_3 |
1 1
o13 : Matrix (R[t ..t ]) <-- (R[t ..t ])
1 19 1 19
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i14 : obstructions D
o14 = 0
1
o14 : Matrix 0 <-- (R[t ..t ])
1 19
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Here is an example of a 4th order approximation of a nested Quot scheme:
i15 : R=QQ[x,y];
|
i16 : F0X=matrix {{x,y,0,0},{0,0,x,y}};
2 4
o16 : Matrix R <-- R
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i17 : F0Y=matrix {{x^2,y^2,0,0,x*y},{0,0,x^2,y^2,0}};
2 5
o17 : Matrix R <-- R
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i18 : D=nestedHilbertScheme(F0X,F0Y,Verbose=>4,HighestOrder=>4,DegreeBound=>1);
Calculating first order relations
Calculating standard expressions for obstructions
Starting lifting
Order 2
Lifting family for X
Calculating tangent cone for obstructions
Calculating residual terms
Lifting Family
Calculating Obstruction Equations
Lifting Relations and Coefficients
Lifting family for Y
Calculating tangent cone for obstructions
Calculating residual terms
Lifting Family
Calculating Obstruction Equations
Lifting Relations and Coefficients
Calculating tangent cone for new obstructions
Calculating joint residual terms
Calculating Joint Obstruction Equations
Changing Families
Changing Relations
Lifting Submodule Relation
Correcting Coefficients
Doing Sanity Check
Checking polynomial lifting
Order 3
Lifting family for X
Calculating tangent cone for obstructions
Calculating residual terms
Lifting Family
Calculating Obstruction Equations
Lifting Relations and Coefficients
Lifting family for Y
Calculating tangent cone for obstructions
Calculating residual terms
Lifting Family
Calculating Obstruction Equations
Lifting Relations and Coefficients
Calculating tangent cone for new obstructions
Calculating joint residual terms
Calculating Joint Obstruction Equations
Changing Families
Changing Relations
Lifting Submodule Relation
Correcting Coefficients
Doing Sanity Check
Checking polynomial lifting
Order 4
Lifting family for X
Calculating tangent cone for obstructions
Calculating residual terms
Lifting Family
Calculating Obstruction Equations
Lifting Relations and Coefficients
Lifting family for Y
Calculating tangent cone for obstructions
Calculating residual terms
Lifting Family
Calculating Obstruction Equations
Lifting Relations and Coefficients
Calculating tangent cone for new obstructions
Calculating joint residual terms
Calculating Joint Obstruction Equations
Changing Families
Changing Relations
Lifting Submodule Relation
Correcting Coefficients
Doing Sanity Check
Checking polynomial lifting
Warning: calculation terminated since HighestOrder has been reached.
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i19 : transpose (families D)_0
o19 = {-1} | t_1+x t_7t_18t_29^2-t_13^2t_17t_31+2t_6t_13t_18t_31-t_12t_13t_
{-1} | t_3+y t_4
{-1} | t_5 t_6+x
{-1} | t_7 t_8+y
-----------------------------------------------------------------------
18t_31+t_5t_13t_25t_31-t_13t_15t_29t_31-t_10t_18t_29t_31-t_13t_14t_31^2
-----------------------------------------------------------------------
-t_9t_18t_31^2+t_6t_18t_29-t_18t_20t_29+t_5t_25t_29+t_18t_26t_29+t_13t_
-----------------------------------------------------------------------
16t_31+t_11t_18t_31-t_18t_19t_31+t_9t_25t_31-t_7t_29t_31-t_5t_31^2+t_
-----------------------------------------------------------------------
10t_31^2+t_18t_21+t_19t_25+t_8t_29-t_27t_29-t_13t_30+t_6t_31-t_12t_31+t
-----------------------------------------------------------------------
_20t_31-t_26t_31+t_2 |
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4 2
o19 : Matrix (R[t ..t ]) <-- (R[t ..t ])
1 31 1 31
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i20 : transpose (families D)_1
o20 = {-2} | t_5t_6t_18t_29-t_5t_18t_20t_29+t_5^2t_25t_29+t_5t_18t_26t_29-t
{-2} | t_3t_7t_13t_25+t_7t_8t_13t_25-t_3t_13t_14t_25-t_1t_13t_15t_25-
{-2} | -t_1t_5-t_5t_6+t_3t_9+t_1t_10+t_7t_11+t_5t_12+yt_5t_13+yt_9+xt
{-2} | -t_3t_7-t_7t_8+t_3t_14+t_1t_15+t_7t_16+t_5t_17+yt_5t_18+yt_14+
{-2} | -t_7t_15t_29^2+t_3t_7t_13t_31+t_7t_8t_13t_31-t_3t_13t_14t_31-t
-----------------------------------------------------------------------
_7^2t_29^2+t_7t_14t_29^2+t_6t_13t_14t_31-t_9t_13t_17t_31+t_5t_11t
t_6t_13t_15t_25-t_7t_13t_16t_25-t_5t_13t_17t_25+t_10t_13t_17t_25+
_10
xt_15
_1t_13t_15t_31-t_6t_13t_15t_31-t_7t_13t_16t_31-t_5t_13t_17t_31+t_
-----------------------------------------------------------------------
_18t_31-t_13t_15t_19t_31-t_5t_18t_19t_31+t_5t_13t_22t_31+t_5t_9t_
t_13t_15t_20t_25-t_5t_13t_23t_25+t_13t_14t_25t_27-t_3t_7t_18t_29-
10t_13t_17t_31+t_13t_15t_20t_31-t_5t_13t_23t_31+t_13t_14t_27t_31+
-----------------------------------------------------------------------
25t_31-t_13t_14t_26t_31-t_5t_7t_29t_31+t_7t_10t_29t_31-t_10t_14t_29t
t_7t_8t_18t_29+t_3t_14t_18t_29+t_1t_15t_18t_29+t_6t_15t_18t_29+t_7t_
t_10t_15t_29t_31+t_9t_15t_31^2-t_6t_15t_29+t_15t_20t_29-t_5t_23t_29-
-----------------------------------------------------------------------
_31-t_5^2t_31^2+t_7t_9t_31^2+t_5t_10t_31^2-t_9t_14t_31^2+t_5t_18t
16t_18t_29+t_5t_17t_18t_29-t_10t_17t_18t_29-t_15t_18t_20t_29+t_5t
t_15t_26t_29+t_7t_27t_29-t_11t_15t_31+t_15t_19t_31-t_9t_23t_31+t_
-----------------------------------------------------------------------
_21+t_5t_19t_25+t_6t_14t_29+t_7t_20t_29-t_14t_20t_29+t_5t_22t_29-2t_7t
_18t_23t_29-t_5t_15t_25t_29+t_10t_15t_25t_29-t_14t_18t_27t_29-t_15^2t_
5t_27t_31-t_10t_27t_31-t_15t_21-t_19t_23+t_26t_27+yt_7t_29+t_10t_30+yt
-----------------------------------------------------------------------
_26t_29+t_14t_26t_29-t_5t_27t_29-t_5t_13t_30+t_1t_5t_31+t_5t_6t_31-t_
29^2+t_9t_15t_25t_31-t_14t_15t_29t_31+t_5t_15t_31^2-t_11t_15t_25-t_9t
_5t_31+yt_26+xt_27+xy
-----------------------------------------------------------------------
3t_9t_31-t_1t_10t_31-t_7t_11t_31-t_5t_12t_31+t_11t_14t_31+t_7t_19t_31-t
_23t_25+t_5t_25t_27-t_10t_25t_27-t_8t_15t_29+t_15t_16t_29-t_15t_22t_29-
-----------------------------------------------------------------------
_14t_19t_31+t_5t_20t_31+t_9t_22t_31-2t_5t_26t_31+t_10t_26t_31+t_14t_
t_7t_23t_29+t_14t_23t_29+2t_15t_27t_29-t_6t_15t_31-t_5t_23t_31+t_15t
-----------------------------------------------------------------------
21+t_19t_22+t_20t_26-t_26^2-t_19t_27+yt_5t_29-t_9t_30+yt_19+xt_20+x2
_26t_31+t_7t_27t_31+t_20t_23+t_10t_24+yt_5t_25-t_23t_26+t_22t_27-t_27^2
-----------------------------------------------------------------------
-t_15t_28+yt_7t_31+yt_22+xt_23+y2
-----------------------------------------------------------------------
-t_13t_16t_19t_25-t_11t_18t_19t_25-t_9t_19t_25^2+t_6^2t_18t_29-t_
t_4t_7t_13t_25+t_8^2t_13t_25-t_4t_13t_14t_25-t_2t_13t_15t_25-t_8t
-t_5t_6t_18t_29+t_6t_10t_18t_29+t_5t_18t_20t_29-t_10t_18t_20t_29-
t_5t_13t_18t_24-t_1t_5t_18t_25-t_5t_6t_18t_25+t_3t_9t_18t_25+t_1t
t_6t_18t_27t_29-t_18t_20t_27t_29+t_5t_25t_27t_29+t_18t_26t_27t_29
-----------------------------------------------------------------------
8t_18t_19t_29+2t_16t_18t_19t_29-t_6t_18t_20t_29-t_18t_19t_22t_29+
_13t_16t_25-2t_6t_13t_17t_25+t_12t_13t_17t_25+yt_13^2t_17t_25-2yt
t_5^2t_25t_29+t_5t_10t_25t_29-t_5t_18t_26t_29+t_10t_18t_26t_29-t_
_10t_18t_25+t_7t_11t_18t_25+t_5t_12t_18t_25-t_11t_14t_18t_25-t_9t
-t_7t_17t_29^2+t_4t_7t_13t_31+t_8^2t_13t_31-t_4t_13t_14t_31-t_2t_
-----------------------------------------------------------------------
t_5t_13t_24t_29+t_5t_12t_25t_29-t_7t_19t_25t_29+t_14t_19t_25t_29+t_6t
_6t_13t_18t_25+yt_12t_13t_18t_25-t_5t_13t_24t_25-yt_5t_13t_25^2+t_13t
5t_13t_16t_31+t_10t_13t_16t_31-t_5t_11t_18t_31+t_10t_11t_18t_31+t_5t_
_18t_22t_25-t_10t_18t_25t_26-t_5t_18^2t_28+t_3t_7t_18t_29+t_7t_8t_18t
13t_15t_31-t_8t_13t_16t_31-2t_6t_13t_17t_31+t_12t_13t_17t_31-t_5t_13t
-----------------------------------------------------------------------
_18t_26t_29-t_5t_25t_26t_29+t_18t_19t_27t_29-t_5t_18t_28t_29-
_15t_25t_28-t_4t_7t_18t_29-t_8^2t_18t_29+t_4t_14t_18t_29+t_2t
18t_19t_31-t_10t_18t_19t_31-t_5t_9t_25t_31+t_9t_10t_25t_31+t_
_29-t_3t_14t_18t_29-t_8t_14t_18t_29-t_1t_15t_18t_29-t_7t_16t_
_24t_31+t_13t_16t_27t_31+t_11t_18t_27t_31-t_18t_19t_27t_31+t_
-----------------------------------------------------------------------
t_7t_8t_29^2+t_7t_16t_29^2-t_5t_17t_29^2+xt_7t_18t_29^2+t_5t_23t_29^2
_15t_18t_29+t_8t_16t_18t_29+2t_6t_17t_18t_29-t_12t_17t_18t_29-yt_13t_
5t_7t_29t_31-t_7t_10t_29t_31+t_5^2t_31^2-2t_5t_10t_31^2+t_10^2t_31^2-
18t_29+t_14t_16t_18t_29-t_5t_17t_18t_29+t_5t_15t_25t_29+t_15t_18t_26t
9t_25t_27t_31+t_13t_15t_28t_31+t_10t_17t_29t_31-t_7t_27t_29t_31+t_13t
-----------------------------------------------------------------------
+t_6t_13t_16t_31-t_11t_13t_17t_31-xt_13^2t_17t_31+t_6t_11t_18t_31+2xt
17t_18t_29+2yt_6t_18^2t_29-yt_12t_18^2t_29+t_6t_18t_23t_29-t_18t_20t_
t_5t_18t_21+t_10t_18t_21-t_5t_19t_25+t_10t_19t_25-t_5t_8t_29+t_8t_10t
_29+t_14t_18t_27t_29+t_13t_15t_16t_31-t_6t_14t_18t_31-t_9t_18t_23t_31
_14t_30t_31+t_9t_17t_31^2-t_5t_27t_31^2+t_10t_27t_31^2+t_18t_21t_27+t
-----------------------------------------------------------------------
_6t_13t_18t_31-xt_12t_13t_18t_31-2t_6t_18t_19t_31+t_5t_18t_21t_31-t
23t_29+t_5t_18t_24t_29+yt_13t_15t_25t_29-t_5t_17t_25t_29+t_10t_17t_
_29+t_5t_27t_29-t_10t_27t_29+t_5t_13t_30-t_10t_13t_30-t_5t_6t_31+t_
+t_9t_15t_25t_31+t_14t_18t_26t_31-t_10t_18t_27t_31-t_7t_15t_29t_31-
_19t_25t_27-t_6t_17t_29+t_17t_20t_29-t_5t_24t_29-t_17t_26t_29+t_8t_
-----------------------------------------------------------------------
_10t_18t_21t_31+t_9t_12t_25t_31+xt_5t_13t_25t_31+t_5t_19t_25t_31-2t_10t
25t_29+yt_10t_18t_25t_29+t_5t_23t_25t_29+t_18t_23t_26t_29-t_15t_18t_28t
6t_10t_31+t_5t_12t_31-t_10t_12t_31-t_5t_20t_31+t_10t_20t_31+t_5t_26t_31
t_5t_15t_31^2+t_10t_15t_31^2+t_9t_18t_24+t_15t_19t_25-t_14t_18t_28+t_8t
27t_29-t_27^2t_29-t_13t_27t_30+t_7t_29t_30-t_11t_17t_31+t_17t_19t_31-t_
-----------------------------------------------------------------------
_19t_25t_31+t_18t_19t_26t_31-t_9t_25t_26t_31-t_9t_18t_28t_31-t_6t_7t_
_29-t_15t_17t_29^2-2yt_15t_18t_29^2+t_13t_14t_25t_30-t_14t_18t_29t_30
-t_10t_26t_31-t_2t_5-t_6^2+t_4t_9+t_2t_10+t_8t_11+t_6t_12+yt_6t_13+yt
_15t_29-t_15t_27t_29-t_13t_15t_30+t_10t_18t_30+t_6t_15t_31-t_12t_15t_
9t_24t_31+t_6t_27t_31-t_12t_27t_31+t_20t_27t_31-t_26t_27t_31+t_5t_30t
-----------------------------------------------------------------------
29t_31-xt_13t_15t_29t_31-t_10t_16t_29t_31-t_9t_17t_29t_31-
+t_13t_16t_23t_31+t_11t_18t_23t_31-t_18t_19t_23t_31+yt_13t
_11+xt_12+xyt_13+x2
31+t_15t_20t_31-t_15t_26t_31-t_4t_7-t_8^2+t_4t_14+t_2t_15+
_31-t_10t_30t_31-t_17t_21-t_19t_24+t_27t_28+yt_8t_29+t_12t
-----------------------------------------------------------------------
xt_10t_18t_29t_31+t_15t_19t_29t_31+t_5t_22t_29t_31+t_9t_23t_29t_31-2t_
_14t_25t_31+t_9t_17t_25t_31+yt_9t_18t_25t_31+t_9t_23t_25t_31-t_14t_17t
t_8t_16+t_6t_17+yt_6t_18+yt_16+xt_17+xyt_18+y2
_30-t_20t_30+t_26t_30+yt_6t_31+yt_28+y2t_29+xt_30+xyt_31
-----------------------------------------------------------------------
5t_27t_29t_31+t_10t_27t_29t_31-t_5t_12t_31^2+t_10t_12t_31^2-xt_13t_14t_
_29t_31-2yt_14t_18t_29t_31-t_7t_23t_29t_31+t_5t_17t_31^2+yt_5t_18t_31^2
-----------------------------------------------------------------------
31^2-t_9t_16t_31^2-xt_9t_18t_31^2+t_7t_19t_31^2+t_5t_20t_31^2-t_10t
-t_5t_23t_31^2+t_10t_23t_31^2+t_18t_21t_23-yt_13t_16t_25-t_11t_17t_
-----------------------------------------------------------------------
_20t_31^2+t_9t_22t_31^2-t_5t_26t_31^2+t_10t_26t_31^2-t_9t_27t_31^2+t_6t
25-yt_11t_18t_25+t_19t_23t_25-t_9t_24t_25-yt_9t_25^2-t_8t_17t_29+t_16t_
-----------------------------------------------------------------------
_18t_21+t_13t_19t_24+t_12t_19t_25-t_19t_25t_26-t_18t_19t_28+t_6t_16t_29
17t_29-yt_8t_18t_29+2yt_16t_18t_29-t_17t_22t_29-yt_18t_22t_29+t_8t_23t_
-----------------------------------------------------------------------
+xt_6t_18t_29-t_17t_19t_29+t_8t_20t_29-t_16t_20t_29-xt_18t_20t_29+t_19t
29-t_7t_24t_29+t_14t_24t_29-yt_7t_25t_29+yt_14t_25t_29+t_17t_27t_29+yt_
-----------------------------------------------------------------------
_23t_29+xt_5t_25t_29-t_8t_26t_29+t_16t_26t_29+xt_18t_26t_29-t_6t_27t_29
18t_27t_29-t_23t_27t_29-t_13t_23t_30+t_5t_25t_30-t_10t_25t_30+t_15t_29t
-----------------------------------------------------------------------
-t_7t_28t_29-t_6t_13t_30+t_5t_29t_30+t_2t_5t_31+t_6^2t_31-t_4t_9t_31-t_
_30-t_6t_17t_31-yt_6t_18t_31+t_6t_23t_31-t_12t_23t_31+t_20t_23t_31-t_5t
-----------------------------------------------------------------------
2t_10t_31-t_8t_11t_31-t_6t_12t_31+t_11t_16t_31+xt_13t_16t_31+xt_11t_
_24t_31-yt_10t_25t_31+t_17t_26t_31+yt_18t_26t_31-t_23t_26t_31+yt_15t
-----------------------------------------------------------------------
18t_31-t_16t_19t_31-xt_18t_19t_31+t_6t_20t_31+t_19t_22t_31+xt_9t_25t_31
_29t_31+t_7t_30t_31+yt_7t_31^2+t_12t_24+yt_13t_24+yt_12t_25-t_24t_26-yt
-----------------------------------------------------------------------
-t_6t_26t_31-t_19t_27t_31-t_5t_28t_31+t_10t_28t_31-xt_7t_29t_31+t_
_25t_26-t_17t_28-yt_18t_28+t_23t_28-yt_17t_29+yt_23t_29+t_22t_30-t
-----------------------------------------------------------------------
9t_30t_31-xt_5t_31^2+xt_10t_31^2+t_16t_21+xt_18t_21+xt_19t_25-t_21t_27+
_27t_30+yt_22t_31-yt_27t_31+xt_24+xyt_25+yt_30+y2t_31
-----------------------------------------------------------------------
t_20t_28-t_26t_28+yt_6t_29+xt_8t_29-xt_27t_29-t_11t_30-xt_13t_30+t_19t_
-----------------------------------------------------------------------
30+xt_6t_31-xt_12t_31+xt_20t_31-xt_26t_31+yt_21+xt_28+xyt_29 |
|
|
|
|
5 2
o20 : Matrix (R[t ..t ]) <-- (R[t ..t ])
1 31 1 31
|
i21 : obstructions D
o21 = | -t_6t_7t_18t_29+t_7t_18t_20t_29-t_5t_7t_25t_29-t_7t_18t_26t_29-t_7t_1
| t_3t_6t_18t_29-t_6t_8t_18t_29-t_3t_18t_20t_29+t_8t_18t_20t_29+t_1t_7t
| -t_3t_5+t_1t_7-t_6t_7+t_5t_8
| t_6t_7t_18t_29-t_7t_18t_20t_29+t_5t_7t_25t_29+t_7t_18t_26t_29+t_7t_13
| 0
| -t_6t_13t_14t_25+t_9t_13t_17t_25-t_5t_11t_18t_25+t_13t_15t_19t_25-t_5
| 0
| -t_6t_13t_16t_25+t_11t_13t_17t_25-t_6t_11t_18t_25-t_5t_18t_21t_25+t_1
| 0
| 0
| 0
| t_6t_13t_14t_23-t_5t_13t_16t_23-t_6t_9t_18t_23+t_5t_11t_18t_23-t_13t_
| -t_2t_7^2t_13+t_1t_7t_8t_13-t_3t_6t_13t_14+t_2t_7t_13t_14+t_2t_5t_13t
| 0
| 0
| t_6t_13t_14t_25-t_9t_13t_17t_25+t_5t_11t_18t_25-t_13t_15t_19t_25+t_5t
| 0
| t_5t_6t_18t_29-t_5t_18t_20t_29+t_5^2t_25t_29+t_5t_18t_26t_29-t_7^2t_2
| -t_13t_16t_19t_25-t_11t_18t_19t_25-t_9t_19t_25^2+t_1t_6t_18t_29+t_6^2
| t_3t_7t_13t_25+t_7t_8t_13t_25-t_3t_13t_14t_25-t_1t_13t_15t_25-t_6t_13
| t_4t_7t_13t_25+t_8^2t_13t_25-t_4t_13t_14t_25-t_2t_13t_15t_25-2t_6t_13
| t_6t_13t_14t_25-t_9t_13t_17t_25+t_5t_11t_18t_25-t_13t_15t_19t_25+t_5t
| t_6t_13t_16t_25-t_11t_13t_17t_25+t_6t_11t_18t_25+t_5t_18t_21t_25-t_10
-----------------------------------------------------------------------
3t_16t_31-t_7t_11t_18t_31+t
_25t_29-t_6t_7t_25t_29+t_3t
t_16t_31+t_7t_11t_18t_31-t_
t_13t_22t_25-t_5t_9t_25^2+t
0t_18t_21t_25-t_9t_12t_25^2
15t_19t_23-t_5t_18t_19t_23+
_15-t_1t_6t_13t_15-t_6t_7t_
_13t_22t_25+t_5t_9t_25^2-t_
9^2+t_7t_14t_29^2+t_6t_13t_
t_18t_29-t_8t_18t_19t_29+2t
t_15t_25-t_5t_13t_17t_25+t_
t_17t_25+t_12t_13t_17t_25+t
_13t_22t_25+t_5t_9t_25^2-t_
t_18t_21t_25+t_9t_12t_25^2+
-----------------------------------------------------------------------
_7t_18t_19t_31-t_7t_9t_25t_31+t_7^2t_29t_31+t_5t_7t_31^2-t_7t_10t_31^2-
_18t_26t_29-t_8t_18t_26t_29+t_3t_13t_16t_31-t_8t_13t_16t_31+t_3t_11t_18
7t_18t_19t_31+t_7t_9t_25t_31-t_7^2t_29t_31-t_5t_7t_31^2+t_7t_10t_31^2+t
_13t_14t_25t_26-t_5t_8t_18t_29+t_6t_14t_18t_29+t_5t_16t_18t_29-t_9t_17t
-t_5t_19t_25^2+t_10t_19t_25^2+t_13t_16t_25t_26+t_11t_18t_25t_26+2t_9t_2
t_10t_18t_19t_23+t_5t_13t_22t_23+t_5t_9t_18t_24-t_3t_7t_9t_25-t_7t_8t_9
13t_16+t_5t_8t_13t_16+t_2t_5^2t_18-t_1t_5t_6t_18+t_3t_6t_9t_18-t_2t_7t_
13t_14t_25t_26+t_5t_8t_18t_29-t_6t_14t_18t_29-t_5t_16t_18t_29+t_9t_17t_
14t_31-t_9t_13t_17t_31+t_5t_11t_18t_31-t_13t_15t_19t_31-t_5t_18t_19t_31
_16t_18t_19t_29-t_1t_18t_20t_29-2t_6t_18t_20t_29+t_18t_20^2t_29-t_18t_1
10t_13t_17t_25+t_7t_11t_18t_25+t_13t_15t_20t_25-t_5t_13t_23t_25+t_7t_9t
_8t_11t_18t_25-t_5t_13t_24t_25+t_8t_9t_25^2+t_13t_15t_25t_28-t_4t_7t_18
13t_14t_25t_26+t_6t_7t_18t_29+t_5t_8t_18t_29-t_6t_14t_18t_29-t_5t_16t_1
t_5t_19t_25^2-t_10t_19t_25^2-t_13t_16t_25t_26-t_11t_18t_25t_26-2t_9t_25
-----------------------------------------------------------------------
t_7t_18t_21-t_7t_19t_25-t_7t_8t_29+t_7t_27t_29+t_7t_13t_30-t_6t_7t_31+t
t_31-t_8t_11t_18t_31-t_3t_18t_19t_31+t_8t_18t_19t_31+t_3t_9t_25t_31-t_8
_7t_18t_21+t_7t_19t_25+t_7t_8t_29-t_7t_27t_29-t_7t_13t_30+t_6t_7t_31-t_
_18t_29-t_15t_18t_19t_29-t_7t_10t_25t_29+t_10t_14t_25t_29-t_14t_18t_26t
5^2t_26+t_9t_18t_25t_28-t_6t_8t_18t_29+2t_6t_16t_18t_29-t_11t_17t_18t_2
t_25+t_3t_9t_14t_25+t_1t_9t_15t_25+t_9t_12t_15t_25+t_7t_9t_16t_25+t_5t_
9t_18-t_2t_5t_10t_18+t_1t_6t_10t_18+t_6t_7t_11t_18-t_5t_8t_11t_18+t_5t_
18t_29+t_15t_18t_19t_29+t_7t_10t_25t_29-t_10t_14t_25t_29+t_14t_18t_26t_
+t_5t_13t_22t_31+t_5t_9t_25t_31-t_13t_14t_26t_31-t_5t_7t_29t_31+t_7t_10
9t_22t_29+t_5t_13t_24t_29+t_1t_5t_25t_29+t_5t_12t_25t_29-t_7t_19t_25t_2
_25^2+t_13t_14t_25t_27-t_3t_7t_18t_29+t_3t_14t_18t_29+t_1t_15t_18t_29+t
t_29+t_4t_14t_18t_29+t_2t_15t_18t_29-t_8t_16t_18t_29+2t_6t_17t_18t_29-t
8t_29+t_9t_17t_18t_29+t_15t_18t_19t_29-t_7t_18t_20t_29+t_5t_7t_25t_29+t
^2t_26-t_9t_18t_25t_28+2t_6t_8t_18t_29-2t_6t_16t_18t_29+t_11t_17t_18t_2
-----------------------------------------------------------------------
_7t_12t_31-t_7t_20t_31+t_7t_26t_31+t_4t_5-t_2t_7
t_9t_25t_31-t_3t_7t_29t_31+t_7t_8t_29t_31-t_1t_7t_31^2+t_6t_7t_31^2+t_3
7t_12t_31+t_7t_20t_31-t_7t_26t_31-t_4t_5+t_2t_7
_29+t_5t_18t_27t_29-t_14t_15t_29^2+t_3t_7t_13t_31+t_7t_8t_13t_31-t_3t_1
9-t_6t_18t_22t_29-t_7t_13t_24t_29+t_13t_14t_24t_29-2t_9t_18t_24t_29-t_7
9t_17t_25-t_9t_10t_17t_25+2t_5t_15t_19t_25-t_10t_15t_19t_25-t_9t_15t_20
14t_18t_21-t_10t_14t_18t_21-t_1t_7t_13t_22+t_6t_7t_13t_22-t_5t_8t_13t_2
29-t_5t_18t_27t_29+t_14t_15t_29^2-t_3t_7t_13t_31-t_7t_8t_13t_31+t_3t_13
t_29t_31-t_10t_14t_29t_31-t_5^2t_31^2+t_7t_9t_31^2+t_5t_10t_31^2-t_9t_1
9+t_14t_19t_25t_29-t_5t_20t_25t_29+t_1t_18t_26t_29+t_6t_18t_26t_29-t_18
_6t_15t_18t_29-t_7t_16t_18t_29+t_5t_17t_18t_29-t_10t_17t_18t_29-t_15t_1
_12t_17t_18t_29+t_8t_18t_22t_29+t_5t_18t_24t_29+t_7t_8t_25t_29-t_8t_14t
_7t_10t_25t_29-t_10t_14t_25t_29+t_7t_18t_26t_29+t_14t_18t_26t_29-t_5t_1
9-t_8t_18t_20t_29+t_6t_18t_22t_29+t_7t_13t_24t_29-t_13t_14t_24t_29+2t_9
-----------------------------------------------------------------------
t_10t_31^2-t_8t_10t_31^2+t_3t_18t_21-t_8t_18t_21+t_3t_19t_25-t_8t_19t_2
3t_14t_31-t_1t_13t_15t_31-t_6t_13t_15t_31-t_7t_13t_16t_31-t_5t_13t_17t_
t_12t_25t_29+t_12t_14t_25t_29-t_5t_16t_25t_29+t_10t_16t_25t_29+t_9t_17t
t_25+t_5t_9t_23t_25-t_13t_14t_23t_26+t_9t_18t_23t_26-t_9t_15t_25t_26-t_
2+t_6t_13t_14t_22-t_5t_13t_16t_22-t_6t_9t_18t_22+t_5t_11t_18t_22+t_5t_1
t_14t_31+t_1t_13t_15t_31+t_6t_13t_15t_31+t_7t_13t_16t_31+t_5t_13t_17t_3
4t_31^2+t_5t_18t_21+t_5t_19t_25+t_6t_14t_29+t_7t_20t_29-t_14t_20t_29+t_
t_20t_26t_29-t_5t_25t_26t_29+t_18t_19t_27t_29-t_5t_18t_28t_29-t_7t_8t_2
8t_20t_29+t_7t_18t_22t_29+t_5t_18t_23t_29+t_7^2t_25t_29-t_7t_14t_25t_29
_25t_29-t_5t_17t_25t_29+t_10t_17t_25t_29-t_8t_18t_27t_29-t_15t_18t_28t_
8t_27t_29-t_7t_15t_29^2+t_14t_15t_29^2+t_7t_13t_16t_31+t_5t_6t_18t_31+t
t_18t_24t_29+t_5t_8t_25t_29+t_7t_12t_25t_29-t_12t_14t_25t_29+t_5t_16t_2
-----------------------------------------------------------------------
5+t_3t_8t_29-t_8^2t_29-t_3t_27t_29+t_8t_27t_29-t_3t_13t_30+t_8t_
31+t_10t_13t_17t_31-t_5t_6t_18t_31+t_13t_15t_20t_31-t_5t_13t_23t
_25t_29-t_15t_19t_25t_29-t_9t_23t_25t_29+t_8t_18t_26t_29-2t_16t_
3t_7t_13t_27-t_7t_8t_13t_27+t_3t_13t_14t_27+t_1t_13t_15t_27+t_6t
3t_22^2-t_1t_5t_13t_23+t_7t_13t_19t_23-t_13t_14t_19t_23+t_9t_18t
1-t_10t_13t_17t_31+t_5t_6t_18t_31-t_13t_15t_20t_31+t_5t_13t_23t_
5t_22t_29-2t_7t_26t_29+t_14t_26t_29-t_5t_27t_29-t_5t_13t_30+t_1t
9^2+t_7t_16t_29^2-t_5t_17t_29^2+t_5t_23t_29^2+t_1t_13t_16t_31+t_
-t_5t_15t_25t_29+t_10t_15t_25t_29-t_7t_18t_27t_29-t_14t_18t_27t_
29-t_15t_17t_29^2+t_13t_14t_25t_30-t_14t_18t_29t_30+t_6t_8t_18t_
_7t_11t_18t_31-t_7t_18t_19t_31+2t_7t_9t_25t_31+t_5t_10t_25t_31-t
5t_29-t_10t_16t_25t_29-t_9t_17t_25t_29+t_15t_19t_25t_29+t_9t_23t
-----------------------------------------------------------------------
13t_30+t_3t_6t_31-t_6t_8t_31-t_3t_12t_31+t_8t_12t_31+t_3t_20t_31-t_8t_2
_31-t_7t_9t_25t_31-t_5t_10t_25t_31+t_9t_14t_25t_31+t_5t_18t_26t_31+t_13
18t_26t_29+t_18t_22t_26t_29+2t_7t_25t_26t_29-2t_14t_25t_26t_29+2t_6t_18
_13t_15t_27+t_7t_13t_16t_27+t_1t_5t_18t_27+t_5t_6t_18t_27-t_3t_9t_18t_2
_19t_23-t_5^2t_13t_24+t_7t_9t_13t_24+t_5t_10t_13t_24+t_9^2t_18t_24+t_1t
31+t_7t_9t_25t_31+t_5t_10t_25t_31-t_9t_14t_25t_31-t_5t_18t_26t_31-t_13t
_5t_31+t_5t_6t_31-t_3t_9t_31-t_1t_10t_31-t_7t_11t_31-t_5t_12t_31+t_11t_
6t_13t_16t_31-t_11t_13t_17t_31+t_1t_11t_18t_31+t_6t_11t_18t_31-t_1t_18t
29-t_15^2t_29^2+t_6t_7t_18t_31+t_7t_10t_25t_31+t_9t_15t_25t_31-t_7t_18t
31+t_8t_10t_25t_31+t_9t_17t_25t_31-t_8t_18t_26t_31-t_8t_15t_29t_31-t_14
_9t_14t_25t_31-t_5t_18t_26t_31-t_7^2t_29t_31-t_7t_14t_29t_31+t_14^2t_29
_25t_29+2t_16t_18t_26t_29-t_18t_22t_26t_29-2t_7t_25t_26t_29+2t_14t_25t_
-----------------------------------------------------------------------
0t_31-t_3t_26t_31+t_8t_26t_31+t_2t_3-t_1t_4+t_4t_6-t_2t_8
t_14t_27t_31+t_7t_14t_29t_31-t_14^2t_29t_31+t_5t_15t_29t_31+t_10t_15t_2
t_27t_29-t_18t_20t_27t_29+2t_5t_25t_27t_29-t_10t_25t_27t_29+t_7t_18t_28
7-t_1t_10t_18t_27-t_6t_10t_18t_27-t_7t_11t_18t_27-t_13t_15t_20t_27-t_5t
_5^2t_25+t_5^2t_6t_25-t_1t_7t_9t_25+t_6t_7t_9t_25-t_5t_8t_9t_25-2t_1t_5
_14t_27t_31-t_7t_14t_29t_31+t_14^2t_29t_31-t_5t_15t_29t_31-t_10t_15t_29
14t_31+t_7t_19t_31-t_14t_19t_31+t_5t_20t_31+t_9t_22t_31-2t_5t_26t_31+t_
_19t_31-2t_6t_18t_19t_31-t_13t_16t_20t_31-t_11t_18t_20t_31+t_18t_19t_20
_26t_31-t_7t_15t_29t_31-t_14t_15t_29t_31-t_7^2t_31^2+t_5t_15t_31^2-t_7t
t_17t_29t_31-t_7t_8t_31^2+t_5t_17t_31^2-t_8t_13t_24+t_6t_8t_25-t_8t_12t
t_31-t_5t_15t_29t_31-t_5t_7t_31^2+t_7t_10t_31^2-t_5t_14t_31^2+t_7t_18t_
26t_29-2t_6t_18t_27t_29+t_18t_20t_27t_29-2t_5t_25t_27t_29+t_10t_25t_27t
-----------------------------------------------------------------------
9t_31+t_5t_14t_31^2+t_9t_15t_31^2+t_5t_13t_24-t_1t_5t_25-t_5t_6t_25+t_3
t_29-t_15t_16t_29^2-t_14t_17t_29^2-t_7t_23t_29^2+t_14t_23t_29^2+t_15t_2
_18t_20t_27+t_10t_18t_20t_27+t_5t_13t_23t_27-t_9t_14t_25t_27-t_13t_14t_
t_10t_25-t_5t_6t_10t_25+t_3t_9t_10t_25+t_1t_10^2t_25-t_5t_7t_11t_25+t_7
t_31-t_5t_14t_31^2-t_9t_15t_31^2-t_5t_13t_24+t_1t_5t_25+t_5t_6t_25-t_3t
10t_26t_31+t_1^2+t_2t_5-t_3t_19-t_1t_20-t_7t_21+t_14t_21+t_19t_22+t_20t
t_31+t_5t_18t_21t_31-t_10t_18t_21t_31+t_1t_9t_25t_31+t_9t_12t_25t_31+t_
_13t_24+t_6t_7t_25-t_7t_12t_25-t_11t_15t_25-t_9t_23t_25+t_7t_25t_26+t_5
_25-t_11t_17t_25-t_9t_24t_25+t_8t_25t_26+t_8t_18t_28+t_16t_17t_29-t_17t
21-t_5t_13t_24+t_1t_5t_25+t_5t_6t_25-t_3t_9t_25-t_1t_10t_25-t_7t_11t_25
_29-t_7t_18t_28t_29+t_15t_16t_29^2-t_7t_17t_29^2+t_14t_17t_29^2+t_7t_23
-----------------------------------------------------------------------
t_9t_25+t_1t_10t_25+t_7t_11t_25+t_5t_12t_25-t_11t_14t_25-t_9t_22t_25-t_
7t_29^2+t_13t_15t_29t_30+t_5t_18t_29t_30-2t_10t_18t_29t_30+t_4t_7t_13t_
27^2+t_9t_18t_27^2-t_5t_14t_18t_28+t_3t_7t_14t_29+t_7t_8t_14t_29-t_3t_1
t_10t_11t_25-t_5^2t_12t_25+t_5t_10t_12t_25+t_5t_11t_14t_25-t_10t_11t_14
_9t_25-t_1t_10t_25-t_7t_11t_25-t_5t_12t_25+t_11t_14t_25+t_9t_22t_25+t_1
_26-t_26^2-t_19t_27-t_5t_28-t_9t_30
5t_19t_25t_31-2t_10t_19t_25t_31-t_9t_20t_25t_31+t_18t_19t_26t_31-t_9t_2
t_25t_27-t_10t_25t_27+t_7t_18t_28-t_8t_15t_29+t_15t_16t_29+t_7t_17t_29-
_22t_29-t_8t_23t_29-t_7t_24t_29+t_14t_24t_29+t_17t_27t_29+t_5t_25t_30-t
-t_5t_12t_25+t_11t_14t_25+t_7t_19t_25+t_9t_22t_25+t_10t_25t_26+t_5t_18t
t_29^2-t_14t_23t_29^2-t_15t_27t_29^2-t_13t_15t_29t_30-t_5t_18t_29t_30+2
-----------------------------------------------------------------------
10t_25t_26-t_5t_18t_28+t_3t_7t_29+t_7t_8t_29-t_3t_14t_29-t_8t_14t_29-t_
31+t_8^2t_13t_31-t_4t_13t_14t_31-t_2t_13t_15t_31-t_8t_13t_16t_31-2t_6t_
4^2t_29+t_5t_8t_15t_29-t_1t_14t_15t_29-t_12t_14t_15t_29-t_7t_14t_16t_29
t_25+t_9t_12t_14t_25+t_9t_11t_15t_25-t_5t_9t_16t_25-t_9^2t_17t_25+t_5t_
0t_25t_26+t_5t_18t_28-t_3t_7t_29-t_7t_8t_29+t_3t_14t_29+t_8t_14t_29+t_1
5t_26t_31-t_9t_18t_28t_31-t_1t_7t_29t_31-t_6t_7t_29t_31-t_10t_16t_29t_3
t_15t_22t_29-2t_7t_23t_29+t_14t_23t_29+2t_15t_27t_29+t_7t_8t_31-t_6t_15
_10t_25t_30+t_15t_29t_30+t_8^2t_31-t_6t_17t_31-t_8t_22t_31-t_5t_24t_31+
_28-t_3t_7t_29+t_3t_14t_29+t_8t_14t_29+t_1t_15t_29+t_7t_16t_29-t_14t_16
t_10t_18t_29t_30+t_8t_13t_16t_31+t_6^2t_18t_31+t_8t_11t_18t_31-t_8t_18t
-----------------------------------------------------------------------
1t_15t_29-t_6t_15t_29-t_7t_16t_29+t_14t_16t_29-t_5t_17t_29+t_15t_20t_29
13t_17t_31+t_12t_13t_17t_31-t_6^2t_18t_31-2t_5t_13t_24t_31-t_10t_12t_25
-t_5t_14t_17t_29+t_10t_14t_17t_29+t_15^2t_19t_29+t_7t_15t_20t_29+t_14t_
14t_19t_25-t_10t_14t_19t_25-t_9t_15t_19t_25+2t_5t_9t_22t_25-t_9t_10t_22
t_15t_29+t_6t_15t_29+t_7t_16t_29-t_14t_16t_29+t_5t_17t_29-t_15t_20t_29-
1-t_9t_17t_29t_31+t_15t_19t_29t_31+t_7t_20t_29t_31+t_5t_22t_29t_31+t_9t
t_31-t_7t_22t_31-t_5t_23t_31+t_15t_26t_31+2t_7t_27t_31+t_3^2+t_4t_7-t_3
t_17t_26t_31+t_8t_27t_31+t_7t_30t_31+t_3t_4+t_4t_8-t_4t_22-t_2t_23-t_6t
t_29+t_5t_17t_29-t_5t_23t_29-t_15t_26t_29-t_14t_27t_29-t_7t_13t_30+t_6t
_19t_31+t_5t_13t_24t_31+t_8t_9t_25t_31+t_10t_12t_25t_31-t_9t_16t_25t_31
-----------------------------------------------------------------------
+t_14t_27t_29-t_6t_14t_31-t_11t_15t_31+
t_31+t_9t_16t_25t_31-t_5t_20t_25t_31+t_
15t_20t_29+t_5t_15t_22t_29+t_7t_10t_23t
t_25+t_9^2t_23t_25-t_7t_8t_13t_26+t_3t_
t_14t_27t_29+t_6t_14t_31+t_11t_15t_31-t
_23t_29t_31-2t_5t_27t_29t_31+t_10t_27t_
t_22-t_1t_23+t_20t_23-t_5t_24+t_10t_24-
_24+t_12t_24-t_24t_26-t_17t_28+t_23t_28
_7t_31-t_7t_12t_31+t_6t_14t_31+t_7t_20t
+t_5t_20t_25t_31-t_10t_20t_25t_31+t_9t_
-----------------------------------------------------------------------
t_15t_19t_31-t_9t_23t_31+t_14t_26t_31-t_10t_27t_31-t_15t_21+t_9t_24-t_1
10t_20t_25t_31-t_9t_22t_25t_31+2t_6t_18t_26t_31+2t_5t_25t_26t_31-t_18t_
_29-t_5t_14t_23t_29-t_10t_14t_23t_29+t_9t_15t_23t_29-2t_7t_15t_26t_29+t
13t_14t_26+t_1t_13t_15t_26+t_6t_13t_15t_26+t_7t_13t_16t_26+t_1t_5t_18t_
_15t_19t_31+t_9t_23t_31-t_14t_26t_31+t_10t_27t_31+t_15t_21-t_9t_24+t_14
29t_31-t_1t_5t_31^2+t_1t_10t_31^2-t_5t_12t_31^2+t_10t_12t_31^2-t_9t_16t
t_23t_26+t_22t_27-t_27^2-t_15t_28-t_7t_30
-t_8t_30+t_22t_30-t_27t_30
_31-t_7t_26t_31-t_14t_26t_31+t_5t_27t_31+t_1t_3+t_2t_7-t_19t_23-t_9t_24
22t_25t_31-2t_6t_18t_26t_31-2t_5t_25t_26t_31+t_18t_26^2t_31-t_13t_16t_2
-----------------------------------------------------------------------
4t_28+t_10t_30
26^2t_31+t_13t_16t_27t_31+t_11t_18t_27t_31-t_18t_19t_27t_31+2t_9t_25t
_14t_15t_26t_29+t_14^2t_27t_29-3t_5t_15t_27t_29-t_5t_13t_15t_30+t_5t_
26+t_5t_6t_18t_26-t_3t_9t_18t_26-t_1t_10t_18t_26-t_6t_10t_18t_26-t_7t
t_28-t_10t_30
_31^2+t_7t_19t_31^2+2t_5t_20t_31^2-2t_10t_20t_31^2+t_9t_22t_31^2-t_5t
-t_3t_26-t_1t_27+t_26t_27-t_7t_28+t_14t_28-t_5t_30
7t_31-t_11t_18t_27t_31+t_18t_19t_27t_31-2t_9t_25t_27t_31-t_5t_18t_28t
-----------------------------------------------------------------------
_27t_31+t_13t_15t_28t_31+t_5t_18t_28t_31+t_7t_8t_29t_31+t_12t_15t_29t
10t_18t_30-t_3t_7t_10t_31-t_7t_8t_10t_31+t_3t_10t_14t_31+t_5t_6t_15t_
_11t_18t_26-t_13t_14t_22t_26+t_9t_18t_22t_26+t_5t_13t_23t_26+t_5t_10t
_26t_31^2+t_10t_26t_31^2-t_9t_27t_31^2+t_1t_18t_21+t_6t_18t_21-t_18t_
_31-2t_7t_8t_29t_31-t_12t_15t_29t_31+t_14t_16t_29t_31-t_5t_17t_29t_31
-----------------------------------------------------------------------
_31-t_14t_16t_29t_31+t_5t_17t_29t_31+t_10t_17t_29t_31-t_15t_20t_29t_
31+t_1t_10t_15t_31-t_5t_12t_15t_31+t_10t_12t_15t_31+t_7t_10t_16t_31+
_25t_26-t_10^2t_25t_26-2t_9t_14t_25t_26-t_13t_15t_26^2-t_5t_18t_26^2
20t_21+t_13t_19t_24+t_1t_19t_25+t_12t_19t_25-t_19t_20t_25-t_19t_25t_
+t_15t_20t_29t_31+t_7t_22t_29t_31-t_14t_22t_29t_31+t_5t_23t_29t_31+t
-----------------------------------------------------------------------
31-t_7t_22t_29t_31+t_14t_22t_29t_31-t_5t_23t_29t_31-t_14t_27t_29t_31+t
t_5t_10t_17t_31-t_10^2t_17t_31+t_7t_15t_19t_31+2t_5t_15t_20t_31-2t_10t
+t_10t_18t_26^2+t_1t_7t_13t_27-t_13t_15t_19t_27-t_5t_18t_19t_27+t_10t_
26-t_18t_19t_28+t_1t_8t_29+t_6t_16t_29-t_17t_19t_29-t_16t_20t_29+t_19t
_14t_27t_29t_31-t_6t_7t_31^2-t_5t_8t_31^2+t_8t_10t_31^2-t_5t_16t_31^2+
-----------------------------------------------------------------------
_13t_14t_30t_31+t_6t_7t_31^2+t_5t_16t_31^2+t_9t_17t_31^2-t_5t_22t_31^2-
_15t_20t_31+t_9t_15t_22t_31+t_7t_9t_23t_31+t_5t_10t_23t_31-t_9t_14t_23t
18t_19t_27-t_5t_9t_25t_27+t_9t_10t_25t_27-t_7t_13t_26t_27+t_7^2t_13t_28
_23t_29-t_8t_26t_29+t_16t_26t_29-t_1t_27t_29-t_6t_27t_29+t_20t_27t_29-t
t_5t_22t_31^2+t_7t_26t_31^2-t_10t_27t_31^2+t_8t_18t_21-t_6t_13t_24+t_2t
-----------------------------------------------------------------------
t_7t_26t_31^2+t_10t_27t_31^2+t_6t_13t_24-t_2t_5t_25-t_6^2t_25+t_
_31-3t_5t_15t_26t_31+t_10t_15t_26t_31-t_10t_14t_27t_31-2t_9t_15t
-t_7t_13t_14t_28-t_5t_13t_15t_28-t_9t_14t_18t_28-t_1t_7^2t_29+t_
_7t_28t_29-t_1t_13t_30-t_6t_13t_30+t_13t_20t_30+t_5t_29t_30+t_2t
_5t_25+t_6^2t_25-t_4t_9t_25-t_2t_10t_25-t_8t_11t_25-t_6t_12t_25+
-----------------------------------------------------------------------
4t_9t_25+t_2t_10t_25+t_8t_11t_25+t_6t_12t_25-t_11t_16t_25-t_13t_24t_26-
_27t_31-t_4t_7t_10-t_8^2t_10+t_3t_7t_12+t_7t_8t_12+t_4t_10t_14-t_3t_12t
6t_7^2t_29-2t_5t_7t_8t_29+t_1t_7t_14t_29-t_6t_7t_14t_29+2t_5t_8t_14t_29
_5t_31+t_1t_6t_31+t_6^2t_31-t_4t_9t_31-t_2t_10t_31-t_8t_11t_31-t_1t_12t
t_11t_16t_25+t_8t_19t_25+t_13t_24t_26+t_12t_25t_26-t_25t_26^2-t_18t_21t
-----------------------------------------------------------------------
t_12t_25t_26+t_25t_26^2+t_18t_21t_27+t_19t_25t_27-t_6t_18t_28+t_5t_25t_
_14+t_2t_5t_15+t_6^2t_15-t_4t_9t_15-t_8t_11t_15-t_1t_12t_15-t_6t_12t_15
-t_8t_10t_14t_29+t_7t_12t_14t_29-t_12t_14^2t_29+2t_1t_5t_15t_29+t_5t_6t
_31-t_6t_12t_31+t_11t_16t_31-t_16t_19t_31+t_1t_20t_31+t_12t_20t_31-t_20
_27-t_19t_25t_27+t_6t_18t_28-t_5t_25t_28+t_10t_25t_28-t_18t_26t_28-t_4t
-----------------------------------------------------------------------
28-t_10t_25t_28+t_18t_26t_28+t_4t_7t_29+t_8^2t_29-t_4t_14t_29-t_2t_15t_
+t_8t_10t_16-t_7t_12t_16-t_1t_5t_17-t_5t_6t_17+t_3t_9t_17+t_1t_10t_17+t
_15t_29-t_3t_9t_15t_29+t_8t_9t_15t_29-t_1t_10t_15t_29+t_5t_7t_16t_29-t_
^2t_31+t_19t_22t_31-t_1t_26t_31-t_6t_26t_31+t_20t_26t_31-t_19t_27t_31-t
_7t_29+t_4t_14t_29+t_2t_15t_29+2t_8t_16t_29-t_16^2t_29+t_6t_17t_29-t_8t
-----------------------------------------------------------------------
29-2t_8t_16t_29+t_16^2t_29-2t_6t_17t_29+t_17t_20t_29+t_8t_
_6t_10t_17+t_7t_11t_17-t_3t_7t_20-t_7t_8t_20+t_3t_14t_20+t
7t_10t_16t_29+t_10t_14t_16t_29-t_9t_15t_16t_29+t_5^2t_17t_
_5t_28t_31+t_10t_28t_31+t_9t_30t_31+t_1t_2+t_2t_6-t_4t_19-
_22t_29+t_16t_22t_29-t_6t_23t_29-t_17t_26t_29+t_23t_26t_29
-----------------------------------------------------------------------
22t_29-t_16t_22t_29+t_6t_23t_29-t_5t_24t_29-t_23t_26t_29+t_16t_27t
_1t_15t_20+t_12t_15t_20+t_7t_16t_20+t_5t_17t_20-t_10t_17t_20-t_15t
29-t_7t_9t_17t_29-t_5t_10t_17t_29+t_9t_14t_17t_29-t_7t_15t_19t_29+
t_2t_20-t_8t_21+t_16t_21-t_21t_27-t_6t_28+t_20t_28-t_26t_28-t_11t_
-t_8t_27t_29-t_16t_27t_29+t_27^2t_29-t_15t_28t_29-t_8t_13t_30+t_9t
-----------------------------------------------------------------------
_29-t_27^2t_29+t_15t_28t_29-t_9t_25t_30-t_13t_27t_30+t_14t_29t_30-
_20^2+t_15t_19t_22+t_1t_5t_23+t_5t_6t_23-t_3t_9t_23-t_1t_10t_23-t_
2t_14t_15t_19t_29-t_5t_15t_20t_29+t_7t_10t_22t_29-t_10t_14t_22t_29
30+t_19t_30
_25t_30+t_13t_27t_30+t_7t_29t_30-t_14t_29t_30+t_6t_8t_31-t_8t_12t_
-----------------------------------------------------------------------
t_6t_16t_31-t_11t_17t_31+t_17t_19t_31+t_6t_22t_31-t_
7t_11t_23-t_5t_12t_23+t_11t_14t_23-t_9t_16t_23-t_14t
+2t_9t_15t_22t_29+2t_7t_9t_23t_29+t_5t_10t_23t_29-t_
31+t_6t_16t_31+t_8t_20t_31-t_6t_22t_31-t_8t_26t_31-t
-----------------------------------------------------------------------
9t_24t_31+t_16t_26t_31-t_22t_26t_31-t_12t_27t_31+t_20t_27t_31+t
_19t_23+t_9t_22t_23+t_15t_20t_26+t_10t_23t_26-t_15t_26^2+t_12t_
9t_14t_23t_29-2t_7t_14t_26t_29+2t_14^2t_26t_29-t_5t_15t_26t_29+
_16t_26t_31+t_22t_26t_31+t_12t_27t_31-t_20t_27t_31-t_7t_28t_31+
-----------------------------------------------------------------------
_7t_28t_31-t_10t_30t_31-t_17t_21+t_21t_23+t_11t_24-t_19t_24-t_16t_28+
14t_27+t_11t_15t_27-t_10t_16t_27-t_9t_17t_27-2t_15t_19t_27-t_14t_20t_
t_10t_15t_26t_29-2t_5t_14t_27t_29+t_10t_14t_27t_29-2t_9t_15t_27t_29-t
t_5t_30t_31+t_1t_4+t_2t_8-t_21t_23-t_11t_24-t_4t_26-t_2t_27-t_8t_28+t
-----------------------------------------------------------------------
t_22t_28+t_12t_30-t_20t_30
27+t_9t_23t_27+t_10t_27^2
_5t_13t_14t_30+t_10t_13t_14t_30-t_9t_13t_15t_30+t_9t_10t_18t_30+t_1t_5t
_16t_28-t_22t_28+t_27t_28-t_6t_30+t_26t_30
-----------------------------------------------------------------------
_7t_31+t_5t_6t_7t_31-2t_3t_7t_9t_31-t_7t_8t_9t_31-t_1t_7t_10t_31-t_7^2t
-----------------------------------------------------------------------
_11t_31-t_5t_7t_12t_31+t_5t_6t_14t_31+t_3t_9t_14t_31-t_6t_10t_14t_31+t_
-----------------------------------------------------------------------
7t_11t_14t_31+t_10t_12t_14t_31+t_1t_9t_15t_31+t_6t_9t_15t_31+t_5t_11t_
-----------------------------------------------------------------------
15t_31-t_5t_10t_16t_31-t_9t_10t_17t_31-t_5t_15t_19t_31-t_10t_15t_19t_31
-----------------------------------------------------------------------
+t_5t_14t_20t_31-t_10t_14t_20t_31+2t_7t_9t_22t_31+t_5t_10t_22t_31+2t_5t
-----------------------------------------------------------------------
_9t_23t_31+t_7t_10t_26t_31-3t_5t_14t_26t_31+t_10t_14t_26t_31-2t_9t_15t_
-----------------------------------------------------------------------
26t_31-t_7t_9t_27t_31-t_9t_14t_27t_31-t_4t_7t_9-t_8^2t_9+t_3t_7t_11+t_
-----------------------------------------------------------------------
7t_8t_11+t_2t_5t_14+t_6^2t_14-t_2t_10t_14-t_3t_11t_14-t_8t_11t_14-t_6t_
-----------------------------------------------------------------------
12t_14+t_2t_9t_15-t_1t_11t_15-t_1t_5t_16-t_5t_6t_16+t_3t_9t_16+t_8t_9t_
-----------------------------------------------------------------------
16+t_1t_10t_16+t_5t_12t_16+t_6t_9t_17-t_5t_11t_17-t_3t_7t_19-t_7t_8t_19
-----------------------------------------------------------------------
+t_3t_14t_19+t_1t_15t_19+t_12t_15t_19+t_7t_16t_19+t_5t_17t_19-t_10t_17t
-----------------------------------------------------------------------
_19-t_15t_19t_20+t_1t_5t_22+t_5t_6t_22-t_3t_9t_22-t_1t_10t_22-t_7t_11t_
-----------------------------------------------------------------------
22-t_5t_12t_22+t_11t_14t_22-t_9t_16t_22+t_9t_22^2+t_10t_19t_23-t_9t_20t
-----------------------------------------------------------------------
_23+t_12t_14t_26+t_11t_15t_26-t_10t_16t_26-t_9t_17t_26-t_15t_19t_26+t_
-----------------------------------------------------------------------
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10t_22t_26+2t_9t_23t_26-t_14t_26^2-t_14t_19t_27-t_9t_22t_27+t_9t_27^2 |
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23 1
o21 : Matrix (R[t ..t ]) <-- (R[t ..t ])
1 31 1 31
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