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Macaulay2
The primary source code repository for Macaulay2, a system for computing in commutative algebra, algebraic geometry and related fields.
If phi: S-->R is a ring homomorphism, M is an S-module and N is an R module, then there is an unambiguous structure of R-module on M\otimes N relative to...
See the code below: ``` restart R = ZZ[i]/(i^2+1) I = ideal"5,i+2" mingens I -- returns | 5 i+2 | minimalPresentation I -- returns ideal (5, 5) ``` This shouldn't...
When accidentally handing an adjacency matrix with negative entries it the "Graphs" package gives output which looks correct, but the edge set is empty. E.g.: ``` A = matrix{{0,-1},{-1,0}} G...
Shouldn't we use the previously cached result here? ``` Macaulay2, version 1.11.1 with packages: ConwayPolynomials, Elimination, IntegralClosure, InverseSystems, LLLBases, PrimaryDecomposition, ReesAlgebra, TangentCone i1 : R=ZZ/101[x,y] o1 = R o1 :...
Loading a package results in opening its raw documentation database file and leaving it open for future access. But the default number of open files for a process can be...
There's something confusing about the makefile in the packages directory. I saw this behavior: a new package had no top level documentation node, and it was referred to in the...
The package RandomObjects exports a symbol called "Certification", which obscures the core symbol of the same name, so that loading RandomObjects first and then a certified package results in an...
R = ZZ[a,x,y] I = ideal(a^2+5, (1+a) * x - 2 * y, 3 * x - (1-a) * y) J = ideal(x * y - x^2 - y^2 -...
Do it better: ``` i1 : R=QQ[x]; i2 : f = matrix {{x}}; g = x * id_(R^1); 1 1 o2 : Matrix R
Let's run the following program: ``` i1 : R=QQ[a..k] o1 = R o1 : PolynomialRing i2 : I=trim ideal(a*b+c*d,a*e+b*f+c*g+d*h); o2 : Ideal of R i3 : M=cokernel gens I o3...
