The following rings are initially present in every session with Macaulay2.
- ZZ -- the class of all integers
- QQ -- the class of all rational numbers
- RR -- the class of all real numbers
- RRi -- the class of all real intervals
- CC -- the class of all complex numbers
The names of some of these rings are double letters so the corresponding symbols with single letters are preserved for use as variables.
Numbers in these rings are constructed as follows.
i1 : 1234
o1 = 1234
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i2 : 123/4
123
o2 = ---
4
o2 : QQ
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i3 : 123.4
o3 = 123.4
o3 : RR (of precision 53)
|
i4 : 1.234e-20
o4 = 1.234e-20
o4 : RR (of precision 53)
|
i5 : 123+4*ii
o5 = 123+4*ii
o5 : CC (of precision 53)
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Integers may be entered in bases 2, 8, or 16 using particular prefixes.
i6 : 0b10011010010 -- binary
o6 = 1234
|
i7 : 0o2322 -- octal
o7 = 1234
|
i8 : 0x4d2 -- hexadecimal
o8 = 1234
|
The usual arithmetic operations are available.
i9 : 4/5 + 2/3
22
o9 = --
15
o9 : QQ
|
i10 : 10^20
o10 = 100000000000000000000
|
i11 : 3*5*7
o11 = 105
|
i12 : 3.1^2.1
o12 = 10.76117160609969
o12 : RR (of precision 53)
|
i13 : sqrt 3.
o13 = 1.732050807568877
o13 : RR (of precision 53)
|
An additional pair of division operations that produce integer quotients and remainders is available.
i14 : 1234//100
o14 = 12
|
i15 : 1234%100
o15 = 34
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Numbers can be promoted to larger rings as follows, see
RingElement _ Ring.
i16 : 1_QQ
o16 = 1
o16 : QQ
|
i17 : (2/3)_CC
o17 = .6666666666666666
o17 : CC (of precision 53)
|
One way to enter real and complex numbers with more precision is to insert the desired number of bits of precision after the letter p at the end of the number, but before the possible e that indicates the exponent of 10.
i18 : 1p300
o18 = 1
o18 : RR (of precision 300)
|
i19 : 1p300e-30
o19 = 1e-30
o19 : RR (of precision 300)
|
Numbers can be lifted to smaller rings as follows, see
lift.
i20 : x = 2/3*ii/ii
o20 = .6666666666666666
o20 : CC (of precision 53)
|
i21 : lift(x,RR)
o21 = .6666666666666666
o21 : RR (of precision 53)
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i22 : lift(x,QQ)
2
o22 = -
3
o22 : QQ
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