How to calculate the wedge product of differential forms with arbitrary coefficients
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I need to calculate the wedge product between some differential forms of the type:
$omega=P_1(x_1, ..., x_n)dx_1+cdots+P_n(x_1, ..., x_n) dx_n$ and $domega$, i-e, $omegawedge domega$.
where each $P_i (x_1, ..., x_n), i=1,ldots,n$ are homogeneous polynomials in $mathbb{C}^n, ngeq4$ (in principle) to try to identify some properties.
How can I implement a routine on Wolfram Mathematica to define the coordinate charts, the variables $x_1, ..., x_n$ and calculate, using the software Mathematica, the wedges products "$omegawedge domega$"?
It would be possible to use arbitrary coefficients in the polynomials $ P_i (x_1, ..., x_5) $, i-e, for instance, $P_1(x_1, ..., x_n) = a_1x_1^3 + a_2x_1x_2^2 + a_5x_5^3 $, where each $ a_i in mathbb{C}$?
graciously
Gilberto Cuzzuol
tensor-products differential-forms exterior-algebra
asked Nov 13 at 16:23
Gilberto Cuzzuol
11
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Gilberto Cuzzuol is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment |
up vote
0
down vote
favorite
I need to calculate the wedge product between some differential forms of the type:
$omega=P_1(x_1, ..., x_n)dx_1+cdots+P_n(x_1, ..., x_n) dx_n$ and $domega$, i-e, $omegawedge domega$.
where each $P_i (x_1, ..., x_n), i=1,ldots,n$ are homogeneous polynomials in $mathbb{C}^n, ngeq4$ (in principle) to try to identify some properties.
How can I implement a routine on Wolfram Mathematica to define the coordinate charts, the variables $x_1, ..., x_n$ and calculate, using the software Mathematica, the wedges products "$omegawedge domega$"?
It would be possible to use arbitrary coefficients in the polynomials $ P_i (x_1, ..., x_5) $, i-e, for instance, $P_1(x_1, ..., x_n) = a_1x_1^3 + a_2x_1x_2^2 + a_5x_5^3 $, where each $ a_i in mathbb{C}$?
graciously
Gilberto Cuzzuol
tensor-products differential-forms exterior-algebra
asked Nov 13 at 16:23
Gilberto Cuzzuol
11
New contributor
Gilberto Cuzzuol is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Maple has packages for doing differential forms and differential systems. I don't think Mathematica has ever bothered implementing such packages.
– Ted Shifrin
Nov 17 at 0:01
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I need to calculate the wedge product between some differential forms of the type:
$omega=P_1(x_1, ..., x_n)dx_1+cdots+P_n(x_1, ..., x_n) dx_n$ and $domega$, i-e, $omegawedge domega$.
where each $P_i (x_1, ..., x_n), i=1,ldots,n$ are homogeneous polynomials in $mathbb{C}^n, ngeq4$ (in principle) to try to identify some properties.
How can I implement a routine on Wolfram Mathematica to define the coordinate charts, the variables $x_1, ..., x_n$ and calculate, using the software Mathematica, the wedges products "$omegawedge domega$"?
It would be possible to use arbitrary coefficients in the polynomials $ P_i (x_1, ..., x_5) $, i-e, for instance, $P_1(x_1, ..., x_n) = a_1x_1^3 + a_2x_1x_2^2 + a_5x_5^3 $, where each $ a_i in mathbb{C}$?
graciously
Gilberto Cuzzuol
tensor-products differential-forms exterior-algebra
asked Nov 13 at 16:23
Gilberto Cuzzuol
11
New contributor
Gilberto Cuzzuol is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I need to calculate the wedge product between some differential forms of the type:
$omega=P_1(x_1, ..., x_n)dx_1+cdots+P_n(x_1, ..., x_n) dx_n$ and $domega$, i-e, $omegawedge domega$.
where each $P_i (x_1, ..., x_n), i=1,ldots,n$ are homogeneous polynomials in $mathbb{C}^n, ngeq4$ (in principle) to try to identify some properties.
How can I implement a routine on Wolfram Mathematica to define the coordinate charts, the variables $x_1, ..., x_n$ and calculate, using the software Mathematica, the wedges products "$omegawedge domega$"?
It would be possible to use arbitrary coefficients in the polynomials $ P_i (x_1, ..., x_5) $, i-e, for instance, $P_1(x_1, ..., x_n) = a_1x_1^3 + a_2x_1x_2^2 + a_5x_5^3 $, where each $ a_i in mathbb{C}$?
graciously
Gilberto Cuzzuol
tensor-products differential-forms exterior-algebra
tensor-products differential-forms exterior-algebra
asked Nov 13 at 16:23
Gilberto Cuzzuol
11
New contributor
Gilberto Cuzzuol is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 13 at 16:23
Gilberto Cuzzuol
11
New contributor
Gilberto Cuzzuol is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 13 at 16:23
Gilberto Cuzzuol
11
New contributor
Gilberto Cuzzuol is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 13 at 16:23
Gilberto Cuzzuol
11
asked Nov 13 at 16:23
Gilberto Cuzzuol
11
11
New contributor
Gilberto Cuzzuol is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Gilberto Cuzzuol is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Gilberto Cuzzuol is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Maple has packages for doing differential forms and differential systems. I don't think Mathematica has ever bothered implementing such packages.
– Ted Shifrin
Nov 17 at 0:01
add a comment |
Maple has packages for doing differential forms and differential systems. I don't think Mathematica has ever bothered implementing such packages.
– Ted Shifrin
Nov 17 at 0:01
Maple has packages for doing differential forms and differential systems. I don't think Mathematica has ever bothered implementing such packages.
– Ted Shifrin
Nov 17 at 0:01
Maple has packages for doing differential forms and differential systems. I don't think Mathematica has ever bothered implementing such packages.
– Ted Shifrin
Nov 17 at 0:01
add a comment |
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Gilberto Cuzzuol is a new contributor. Be nice, and check out our Code of Conduct.
Gilberto Cuzzuol is a new contributor. Be nice, and check out our Code of Conduct.
Gilberto Cuzzuol is a new contributor. Be nice, and check out our Code of Conduct.
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Maple has packages for doing differential forms and differential systems. I don't think Mathematica has ever bothered implementing such packages.
– Ted Shifrin
Nov 17 at 0:01