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It seems you are confusing calls to SparseMatrixProduct and SparseMatrixPower. Indeed, SparseMatrixPower(A,A) is meaningless (the second argument should be an integer not a matrix).

When p is odd, your code try to make two steps at once (see the (p-1)/2). To understand the algorithm that is behind your code, I would suggest to separate the add/multiply (p- > p-1) part and the double/squaring (p->p/2) part as follows :

sage: def SparseMatrixPower(A,p):
....:     if p == 1: 
....:         return(A)
....:     elif Mod(p,2):
....:         return SparseMatrixProduct(A,SparseMatrixPower(A,p-1))
....:     else:
....:         return SparseMatrixPower(SparseMatrixProduct(A,A), p / 2)

That said, if you plan to play a lot with twose objects, I would suggest to define a class for them and define a __mul__ method to define the product. Then Sage has generic double-and-add (or multiply-and-square) to automatically define the power, see for example https://doc.sagemath.org/html/en/reference/rings_standard/sage/arith/power.html

It seems you are confusing calls to SparseMatrixProduct and SparseMatrixPower. Indeed, SparseMatrixPower(A,A) is meaningless (the second argument should be an integer not a matrix).

When p is odd, your code try to make two steps at once (see the (p-1)/2). To understand the algorithm that is behind your code, I would suggest to separate the add/multiply (p- > p -> p-1) part and the double/squaring (p->p/2p -> p/2) part as follows :

sage: def SparseMatrixPower(A,p):
....:     if p == 1: 
....:         return(A)
....:     elif Mod(p,2):
....:         return SparseMatrixProduct(A,SparseMatrixPower(A,p-1))
....:     else:
....:         return SparseMatrixPower(SparseMatrixProduct(A,A), p / 2)

That said, if you plan to play a lot with twose objects, I would suggest to define a class for them and define a __mul__ method to define the product. Then Sage has generic double-and-add (or multiply-and-square) to automatically define the power, see for example https://doc.sagemath.org/html/en/reference/rings_standard/sage/arith/power.html

It seems you are confusing calls to SparseMatrixProduct and SparseMatrixPower. Indeed, SparseMatrixPower(A,A) is meaningless (the second argument should be an integer not a matrix).

When p is odd, your code try to make two steps at once (see the (p-1)/2). To understand the algorithm that is behind your code, I would suggest to separate the add/multiply (p -> p-1) part and the double/squaring (p -> p/2) part as follows :

sage: def SparseMatrixPower(A,p):
SparseMatrixPower(A, p):
....:     if p == 1: 
....:         return(A)
....:     elif Mod(p,2):
Mod(p, 2):
....:         return SparseMatrixProduct(A,SparseMatrixPower(A,p-1))
SparseMatrixProduct(A, SparseMatrixPower(A, p-1))
....:     else:
....:         return SparseMatrixPower(SparseMatrixProduct(A,A), p / 2)
SparseMatrixPower(SparseMatrixProduct(A, A), p/2)

That said, if you plan to play a lot with twose objects, I would suggest to define a class for them and define a __mul__ method to define the product. Then Sage has generic double-and-add (or multiply-and-square) to automatically define the power, see for example https://doc.sagemath.org/html/en/reference/rings_standard/sage/arith/power.html

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