makeB'Slice -- makeB'Slice creates a hash table that represents a linear slice.

Synopsis

Usage:

makeB'Slice(sliceType,variableGroups)
Inputs:
- sliceType, a list, A list of integers or integer.
- variableGroups, a list, A list of list of variables or list of variables.
Optional inputs:
- B'Homogenization => ..., default value {}, makeB'Section creates a hash table that represents a hyperplane.
- B'NumberCoefficients => ..., default value {}
- ContainsMultiProjectivePoint => ..., default value {}
- ContainsPoint => ..., default value {}
- NameB'Slice => ..., default value null
- RandomCoefficientGenerator => ..., default value FunctionClosure[../../../../../Macaulay2/packages/Bertini.m2:2356:37-2356:66]

Description

makeB'Slice allows for easy creation of equations that define linear spaces, i.e. slices. The default creates a hash table with two keys: B'NumberCoefficients and B'SectionString. When we have a multiprojective variety we can different types of slices. To make a slice we need to specify the type of slice we want followed by variable groups.

i1 : sliceType={1,1}

o1 = {1, 1}

o1 : List

i2 : variableGroups={{x0,x1},{y0,y1,y2}}

o2 = {{x0, x1}, {y0, y1, y2}}

o2 : List

i3 : xySlice=makeB'Slice(sliceType,variableGroups)

o3 = B'Slice{...4...}

o3 : B'Slice

i4 : peek xySlice

o4 = B'Slice{B'NumberCoefficients => {{1.49144+.713846*ii, -.840113+1.1986*ii}, {.014842+1.23548*ii, -.214468+.911293*ii, -.486176+.400577*ii}}                       }
             B'SectionString => {(1.49144+.713846*ii)*(x0)+(-.840113+1.1986*ii)*(x1), (.014842+1.23548*ii)*(y0)+(-.214468+.911293*ii)*(y1)+(-.486176+.400577*ii)*(y2)}
             ListB'Sections => {B'Section{...2...}, B'Section{...2...}}
             NameB'Slice => null

i5 : for i in  xySlice#B'SectionString do print i
(1.49144+.713846*ii)*(x0)+(-.840113+1.1986*ii)*(x1)
(.014842+1.23548*ii)*(y0)+(-.214468+.911293*ii)*(y1)+(-.486176+.400577*ii)*(y2)

i6 : aSlice=makeB'Slice(3,{x,y,z,1},NameB'Slice=>"f");

i7 : aSlice#NameB'Slice

o7 = {f0, f1, f2}

o7 : List

i8 : makeB'InputFile(storeBM2Files,AffVariableGroup=>{x,y,z},B'Functions=>{aSlice},NamePolynomials=>{"f0","f1","f2"});

i9 : f1="x0*y0+x1*y0+x2*y2"

o9 = x0*y0+x1*y0+x2*y2

i10 : f2="x0*y0^2+x1*y1*y2+x2*y0*y2"

o10 = x0*y0^2+x1*y1*y2+x2*y0*y2

i11 : variableGroups={{x0,x1,x2},{y0,y1,y2}}

o11 = {{x0, x1, x2}, {y0, y1, y2}}

o11 : List

i12 : xxSlice=makeB'Slice({2,0},variableGroups)

o12 = B'Slice{...4...}

o12 : B'Slice

i13 : xySlice=makeB'Slice({1,1},variableGroups)

o13 = B'Slice{...4...}

o13 : B'Slice

i14 : yySlice=makeB'Slice({0,2},variableGroups)

o14 = B'Slice{...4...}

o14 : B'Slice

i15 : makeB'InputFile(storeBM2Files,
          HomVariableGroup=>variableGroups,
          B'Polynomials=>{f1,f2}|xxSlice#ListB'Sections);

i16 : runBertini(storeBM2Files)

i17 : xxDegree=#importSolutionsFile(storeBM2Files)

o17 = 2

i18 : makeB'InputFile(storeBM2Files,
          HomVariableGroup=>variableGroups,
          B'Polynomials=>{f1,f2}|xySlice#ListB'Sections);

i19 : runBertini(storeBM2Files)

i20 : xyDegree=#importSolutionsFile(storeBM2Files)

o20 = 3

i21 : makeB'InputFile(storeBM2Files,
          HomVariableGroup=>variableGroups,
          B'Polynomials=>{f1,f2}|yySlice#ListB'Sections);

i22 : runBertini(storeBM2Files)

i23 : yyDegree=#importSolutionsFile(storeBM2Files)

o23 = 1

Ways to use makeB'Slice:

makeB'Slice(Thing,List)

For the programmer

The object makeB'Slice is a method function with options.