>From here <https://stackoverflow.com/a/51636453/4999991> I could solve the
problem:
from itertools import product
from sympy import IndexedBase, symbols, Poly
D=[2,3]
d=len(D)
indices=list(product(*map(range, D)))
a = IndexedBase('a')
coeffs = {i: a[i] for i in indices}
vars = symbols(f'x1:{d+1}')
Poly(coeffs, *vars)
and the result is:
Poly(a[1, 2]*x1*x2**2 + a[1, 1]*x1*x2 + a[1, 0]*x1 + a[0, 2]*x2**2 +
a[0, 1]*x2 + a[0, 0], x1, x2, domain='EX')
On Wed, Aug 1, 2018 at 4:20 PM Foad Sojoodi Farimani <[email protected]>
wrote:
> I think I solved the second problem. From here
> <https://gist.github.com/celliern/c715151a247dbb3c8caec15aeb9af83d> I
> learned that if I change `symbols('x:3')` to `symbols(f'x1:{d+1}')` the
> second issue is solved.
>
> On Wed, Aug 1, 2018 at 3:42 PM Foad Sojoodi Farimani <
> [email protected]> wrote:
>
>> Dear Kalevi,
>>
>> First of thanks a lot for the great instructions. It is a good step
>> forward. I applied your code as:
>>
>> from itertools import product
>> from sympy import IndexedBase, symbols, Poly
>> d=3
>> l=4
>> indices = [i for i in product(range(l), repeat=d) if sum(i) < l]
>> a = IndexedBase('a')
>> coeffs = {i: a[i] for i in indices}
>> vars = symbols('x:3')
>> Poly(coeffs, *vars)
>>
>>
>> However there are a couple of issues:
>>
>> - ` if sum(i) < l ` causes the total degree of each monomial to be
>> less than 4, that's not what I want. I want to take a list or ndarray of
>> non-negative integers D=[d1,...,dm] and each monomial should have a degree
>> of i_j for x_j which is less than d_j , so not the total degree of each
>> monomial but the degree of each variable is important. is there any way to
>> tell `itertools.product` to give the Cartesian product of a list of
>> ranges.
>> something like itertools.product(range(d1),...,range(dm)).
>> - in the second line from bottom how can I change the `3` with a
>> variable?
>>
>> Thanks for your help again.
>>
>> Best,
>> Foad
>>
>>
>>
>>
>> On Wed, Aug 1, 2018 at 3:10 PM Kalevi Suominen <[email protected]> wrote:
>>
>>> I would first generate the list of monomial indices by using e.g.
>>> itertool.product, then create a dictionary containing the indexed
>>> coefficients, and finally create a Poly object with given variables from
>>> those coefficients. For example, to construct a polynomial of degree 3 or
>>> less in 3 variables this could be done:
>>>
>>> indices = [i for i in itertools.product(range(4), repeat=3) if sum(i) <
>>> 4]
>>> a = IndexBase('a')
>>> coeffs = {i: a[i] for i in indices}
>>> vars = symbols('x:3')
>>> Poly(coeffs, *vars)
>>>
>>> Kalevi Suominen
>>>
>>> On Wednesday, August 1, 2018 at 2:01:13 PM UTC+3, foadsf wrote:
>>>>
>>>> I want to use power series to approximate some PDEs. The first step I
>>>> need to generate symbolic multivariate polynomials, given a numpy ndarray.
>>>>
>>>> Consider the polynomial below:
>>>>
>>>> <https://i.stack.imgur.com/eBQVK.png>
>>>>
>>>>
>>>> I want to take a m dimensional ndarray of D=[d1,...,dm] where djs are
>>>> non-negative integers, and generate a symbolic multivariate polynomial in
>>>> the form of symbolic expression. The symbolic expression consists of
>>>> monomials of the form:
>>>>
>>>> <https://i.stack.imgur.com/pvDDT.png>
>>>>
>>>>
>>>> Fo example if D=[2,3] the output should be
>>>>
>>>> <https://i.stack.imgur.com/nDhGD.png>
>>>>
>>>>
>>>> For this specific case I could nest two for loops and add the
>>>> expressions. But I don't know what to do for Ds with arbitrary length.
>>>> If I could generate the D dimensional ndarrays of A and X without
>>>> using for loops, then I could use np.sum(np.multiply(A,X)) as Frobenius
>>>> inner product <https://en.wikipedia.org/wiki/Frobenius_inner_product> to
>>>> get what I need.
>>>>
>>>> I would appreciate if you could help me know how to do this in SymPy.
>>>> Thanks in advance.
>>>>
>>> --
>>> You received this message because you are subscribed to the Google
>>> Groups "sympy" group.
>>> To unsubscribe from this group and stop receiving emails from it, send
>>> an email to [email protected].
>>> To post to this group, send email to [email protected].
>>> Visit this group at https://groups.google.com/group/sympy.
>>> To view this discussion on the web visit
>>> https://groups.google.com/d/msgid/sympy/1c70ac48-9c09-43b5-9374-15acb37d2860%40googlegroups.com
>>> <https://groups.google.com/d/msgid/sympy/1c70ac48-9c09-43b5-9374-15acb37d2860%40googlegroups.com?utm_medium=email&utm_source=footer>
>>> .
>>> For more options, visit https://groups.google.com/d/optout.
>>>
>>
--
You received this message because you are subscribed to the Google Groups
"sympy" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at https://groups.google.com/group/sympy.
To view this discussion on the web visit
https://groups.google.com/d/msgid/sympy/CADjqfdqDw9-qqEQ7sFor%3Dm%3DsmMoqnvmrHTqzsOmEV-bsxaox7Q%40mail.gmail.com.
For more options, visit https://groups.google.com/d/optout.
