58 lines
2.0 KiB
Python
58 lines
2.0 KiB
Python
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def magma_module_decomposition(A, B, text = False, prefix="", sufix="", matrices=True):
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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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p = q.factor()[0][0]
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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 = prefix
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if q != p:
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result += "F<a> := GF(" + str(q) + ");"
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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 += "L := IndecomposableSummands(M); L;"
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if matrices:
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result += "for i in [1 .. #L] do print(Generators(Action(L[i]))); end for;"
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result += sufix
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if text:
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return result
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return(magma_free(result))
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def magma_is_isomorphic(A1, B1, A2, B2, text=0):
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q = parent(A1).base_ring().order()
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p = q.factor()[0][0]
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n = A1.dimensions()[0]
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A1 = str(list(A1))
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B1 = str(list(B1))
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A2 = str(list(A2))
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B2 = str(list(B2))
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A1 = A1.replace("(", "")
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A1 = A1.replace(")", "")
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A2 = A2.replace("(", "")
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A2 = A2.replace(")", "")
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B1 = B1.replace("(", "")
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B1 = B1.replace(")", "")
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B2 = B2.replace("(", "")
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B2 = B2.replace(")", "")
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result = ""
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if q != p:
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result += "F<a> := GF(" + str(q) + ");"
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result += "A1 := MatrixAlgebra<GF("+str(q) + "),"+ str(n) + "|"
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result += A1 + "," + B1
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result += ">;"
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result += "M1 := RModule(RSpace(GF("+str(q)+")," + str(n) + "), A1);"
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result += "A2 := MatrixAlgebra<GF("+str(q) + "),"+ str(n) + "|"
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result += A2 + "," + B2
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result += ">;"
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result += "M2 := RModule(RSpace(GF("+str(q)+")," + str(n) + "), A2);"
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result += "IsIsomorphic(M1, M2);"
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if text:
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return result
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return(magma_free(result))
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