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2021-02-01 09:49:00 +0200 asked a question how to sum sums

I am new to sagemath and I am trying to calculate some formulas using it.

I learned how to write a sum such as

sage: a = [2, 2, 3, 4] 
sage: d = [2, 4, 5, 6] 
sage: def pi(i): 
....:      var("i")
....:      f = sum([a[k]*d[k] for k in range(i + 1)])
....:      return f

However, I am having difficulties to write a sum for pi(i) such as

sage: def Z(a, b): 
....:      var("a b")
....:      l = len(d) - 1 
....:      def pi(i):
....:          var("i")
....:          f = sum([a[k]*d[k] for k in range(i + 1)])
....:          return f
....:      h = sum([pi(i) for i in range(l - 1)])
....:      return h

but I got error. I tried to use

for i in range(l - 1):

also it doesn't work.

2020-12-03 11:01:45 +0200 commented answer counting number of matrices in finite field

thank you so much for helping me you are the best :)

2020-12-03 10:59:19 +0200 received badge  Scholar (source)
2020-12-02 20:21:13 +0200 commented answer counting number of matrices in finite field

Thank you for answering my question. I am trying to count them on modules like M=matrix([[x1,x2],[x3,-x1]]) or M=matrix([x1,x2,x3],[x4,x5,x6],[x7,x8,-x1-x5]]) Is there a way where I can put the variables and make sage run them through GF(p)

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2020-12-02 17:18:01 +0200 asked a question counting number of matrices in finite field

I am new to sage and I want to count the number of matrices per rank in a given finite field.

Example: M=matrix([[x1, x2, x3],[ x4,-x1, x5],[x6,x7,x8]]) in Z/3Z