56 lines
2.0 KiB
Python
56 lines
2.0 KiB
Python
def magmathis(A, B, text = False):
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"""Find decomposition of Z/p^2-module given by matrices A, B into indecomposables using magma.
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If text = True, print the command for Magma. Else - return the output of Magma free."""
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q = parent(A).base_ring().order()
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n = A.dimensions()[0]
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A = str(list(A))
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B = str(list(B))
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A = A.replace("(", "")
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A = A.replace(")", "")
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B = B.replace("(", "")
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B = B.replace(")", "")
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result = "A := MatrixAlgebra<GF("+str(q) + "),"+ str(n) + "|"
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result += A + "," + B
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result += ">;"
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result += "M := RModule(RSpace(GF("+str(q)+")," + str(n) + "), A);"
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result += "IndecomposableSummands(M);"
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if text:
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return result
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print(magma_free(result))
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def as_reduction(AS, fct):
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n = AS.height
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F = AS.base_ring
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variable_names = 'x, y'
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for i in range(n):
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variable_names += ', z' + str(i)
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Rxyz = PolynomialRing(F, n+2, variable_names)
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x, y = Rxyz.gens()[:2]
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z = Rxyz.gens()[2:]
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RxyzQ = FractionField(Rxyz)
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ff = AS.functions
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ff = [RxyzQ(F.function) for F in ff]
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fct = RxyzQ(fct)
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fct1 = numerator(fct)
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fct2 = denominator(fct)
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if fct2 != 1:
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return as_reduction(AS, fct1)/as_reduction(AS, fct2)
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result = RxyzQ(0)
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change = 0
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for a in fct1.monomials():
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degrees_zi = [a.degree(z[i]) for i in range(n)]
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d_div = [a.degree(z[i])//p for i in range(n)]
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if d_div != n*[0]:
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change = 1
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d_rem = [a.degree(z[i])%p for i in range(n)]
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monomial = fct1.coefficient(a)*x^(a.degree(x))*y^(a.degree(y))*prod(z[i]^(d_rem[i]) for i in range(n))*prod((z[i] + ff[i])^(d_div[i]) for i in range(n))
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result += RxyzQ(fct1.coefficient(a)*x^(a.degree(x))*y^(a.degree(y))*prod(z[i]^(d_rem[i]) for i in range(n))*prod((z[i] + ff[i])^(d_div[i]) for i in range(n)))
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if change == 0:
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return RxyzQ(result)
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else:
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print(fct, '\n')
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return as_reduction(AS, RxyzQ(result)) |