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Is there a certain program with which I could make several substitutions in a very large algebraic...
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I'm doing some fairly basic (but incredibly messy) mathematics that involves a lot of algebra. I've gotten to a point where I need to substitute certain sets of variables to make the expressions more manageable, then take sets of those substitutions and make more substitutions.
I want to be able to replace all of those substitutions with the original variables without having to type them all out myself (because some of the expressions contain more than 150 variables). If I could replace all of the substitutions with the original variables, I'd potentially find ways to simplify the expressions, and I'd be able to write programs involving these expressions without having to write definitions for each substitution.
The other issue is that there are multiple expressions of the same form, but with different variables. So I'm essentially writing the same thing but with different subscripts. So say I have an expression containing several of each of the following variables: x_1, x_2, y_1, y_2. What I would want to be able to do is make a copy of the expression then replace all x_1's with x_3's, all x_2's with x_4's, etc.
I'd also want to be able to replace an entire expression with some other expression or a dependent variable.
For instance:
- a_1 = (x_1-x_2)
- a_2 = (x_3-x_4)
- b_1 = (y_1-y_2)
- b_2 = (y_3-y_4)
(x_1-x_2)(x_3-x_4)/((y_1-y_2)(y_3-y_4)) = (a_1)(a_2)/((b_1)(b_2))
In reality, the expressions I'm dealing with have several of each x or y and each a or b is equivalent to 3 or 4 different x's and y's with 2 or 3 different operations acting on the x's and y's. Even after all the x's and y's are replaced by a's and b's, there might be several of the same a or b (i.e. several of each of a_1, a_2, b_1, etc.). I might see that some of these variables are often found in a certain arrangement, so I equate them to yet another variable (i.e. A_1=(a_1+a_2)^2). And the resulting expression still contains maybe 10-20 different variables.
I can't just use Word primarily because I need to be able to perform a "search and replace" in specific expressions. The secondary reason is because word can't (effectively at least) deal with standard mathematical notation like fraction bars and roots.
math-software computer-algebra-systems
asked 2 days ago
TruncatedIcosahedron
11
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I'm doing some fairly basic (but incredibly messy) mathematics that involves a lot of algebra. I've gotten to a point where I need to substitute certain sets of variables to make the expressions more manageable, then take sets of those substitutions and make more substitutions.
I want to be able to replace all of those substitutions with the original variables without having to type them all out myself (because some of the expressions contain more than 150 variables). If I could replace all of the substitutions with the original variables, I'd potentially find ways to simplify the expressions, and I'd be able to write programs involving these expressions without having to write definitions for each substitution.
The other issue is that there are multiple expressions of the same form, but with different variables. So I'm essentially writing the same thing but with different subscripts. So say I have an expression containing several of each of the following variables: x_1, x_2, y_1, y_2. What I would want to be able to do is make a copy of the expression then replace all x_1's with x_3's, all x_2's with x_4's, etc.
I'd also want to be able to replace an entire expression with some other expression or a dependent variable.
For instance:
- a_1 = (x_1-x_2)
- a_2 = (x_3-x_4)
- b_1 = (y_1-y_2)
- b_2 = (y_3-y_4)
(x_1-x_2)(x_3-x_4)/((y_1-y_2)(y_3-y_4)) = (a_1)(a_2)/((b_1)(b_2))
In reality, the expressions I'm dealing with have several of each x or y and each a or b is equivalent to 3 or 4 different x's and y's with 2 or 3 different operations acting on the x's and y's. Even after all the x's and y's are replaced by a's and b's, there might be several of the same a or b (i.e. several of each of a_1, a_2, b_1, etc.). I might see that some of these variables are often found in a certain arrangement, so I equate them to yet another variable (i.e. A_1=(a_1+a_2)^2). And the resulting expression still contains maybe 10-20 different variables.
I can't just use Word primarily because I need to be able to perform a "search and replace" in specific expressions. The secondary reason is because word can't (effectively at least) deal with standard mathematical notation like fraction bars and roots.
math-software computer-algebra-systems
asked 2 days ago
TruncatedIcosahedron
11
New contributor
TruncatedIcosahedron is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
Mathematica (Wolfram language) is great at this. You can set up a trial online account if you're just looking to do a handful of things.
– Kelly Lowder
2 days ago
add a comment |
up vote
0
down vote
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up vote
0
down vote
favorite
I'm doing some fairly basic (but incredibly messy) mathematics that involves a lot of algebra. I've gotten to a point where I need to substitute certain sets of variables to make the expressions more manageable, then take sets of those substitutions and make more substitutions.
I want to be able to replace all of those substitutions with the original variables without having to type them all out myself (because some of the expressions contain more than 150 variables). If I could replace all of the substitutions with the original variables, I'd potentially find ways to simplify the expressions, and I'd be able to write programs involving these expressions without having to write definitions for each substitution.
The other issue is that there are multiple expressions of the same form, but with different variables. So I'm essentially writing the same thing but with different subscripts. So say I have an expression containing several of each of the following variables: x_1, x_2, y_1, y_2. What I would want to be able to do is make a copy of the expression then replace all x_1's with x_3's, all x_2's with x_4's, etc.
I'd also want to be able to replace an entire expression with some other expression or a dependent variable.
For instance:
- a_1 = (x_1-x_2)
- a_2 = (x_3-x_4)
- b_1 = (y_1-y_2)
- b_2 = (y_3-y_4)
(x_1-x_2)(x_3-x_4)/((y_1-y_2)(y_3-y_4)) = (a_1)(a_2)/((b_1)(b_2))
In reality, the expressions I'm dealing with have several of each x or y and each a or b is equivalent to 3 or 4 different x's and y's with 2 or 3 different operations acting on the x's and y's. Even after all the x's and y's are replaced by a's and b's, there might be several of the same a or b (i.e. several of each of a_1, a_2, b_1, etc.). I might see that some of these variables are often found in a certain arrangement, so I equate them to yet another variable (i.e. A_1=(a_1+a_2)^2). And the resulting expression still contains maybe 10-20 different variables.
I can't just use Word primarily because I need to be able to perform a "search and replace" in specific expressions. The secondary reason is because word can't (effectively at least) deal with standard mathematical notation like fraction bars and roots.
math-software computer-algebra-systems
asked 2 days ago
TruncatedIcosahedron
11
New contributor
TruncatedIcosahedron is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I'm doing some fairly basic (but incredibly messy) mathematics that involves a lot of algebra. I've gotten to a point where I need to substitute certain sets of variables to make the expressions more manageable, then take sets of those substitutions and make more substitutions.
I want to be able to replace all of those substitutions with the original variables without having to type them all out myself (because some of the expressions contain more than 150 variables). If I could replace all of the substitutions with the original variables, I'd potentially find ways to simplify the expressions, and I'd be able to write programs involving these expressions without having to write definitions for each substitution.
The other issue is that there are multiple expressions of the same form, but with different variables. So I'm essentially writing the same thing but with different subscripts. So say I have an expression containing several of each of the following variables: x_1, x_2, y_1, y_2. What I would want to be able to do is make a copy of the expression then replace all x_1's with x_3's, all x_2's with x_4's, etc.
I'd also want to be able to replace an entire expression with some other expression or a dependent variable.
For instance:
- a_1 = (x_1-x_2)
- a_2 = (x_3-x_4)
- b_1 = (y_1-y_2)
- b_2 = (y_3-y_4)
(x_1-x_2)(x_3-x_4)/((y_1-y_2)(y_3-y_4)) = (a_1)(a_2)/((b_1)(b_2))
In reality, the expressions I'm dealing with have several of each x or y and each a or b is equivalent to 3 or 4 different x's and y's with 2 or 3 different operations acting on the x's and y's. Even after all the x's and y's are replaced by a's and b's, there might be several of the same a or b (i.e. several of each of a_1, a_2, b_1, etc.). I might see that some of these variables are often found in a certain arrangement, so I equate them to yet another variable (i.e. A_1=(a_1+a_2)^2). And the resulting expression still contains maybe 10-20 different variables.
I can't just use Word primarily because I need to be able to perform a "search and replace" in specific expressions. The secondary reason is because word can't (effectively at least) deal with standard mathematical notation like fraction bars and roots.
math-software computer-algebra-systems
math-software computer-algebra-systems
asked 2 days ago
TruncatedIcosahedron
11
New contributor
TruncatedIcosahedron is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
TruncatedIcosahedron
11
New contributor
TruncatedIcosahedron is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
TruncatedIcosahedron
11
New contributor
TruncatedIcosahedron is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
TruncatedIcosahedron
11
asked 2 days ago
TruncatedIcosahedron
11
11
New contributor
TruncatedIcosahedron is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
TruncatedIcosahedron is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
TruncatedIcosahedron is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
Mathematica (Wolfram language) is great at this. You can set up a trial online account if you're just looking to do a handful of things.
– Kelly Lowder
2 days ago
add a comment |
1
Mathematica (Wolfram language) is great at this. You can set up a trial online account if you're just looking to do a handful of things.
– Kelly Lowder
2 days ago
1
1
Mathematica (Wolfram language) is great at this. You can set up a trial online account if you're just looking to do a handful of things.
– Kelly Lowder
2 days ago
Mathematica (Wolfram language) is great at this. You can set up a trial online account if you're just looking to do a handful of things.
– Kelly Lowder
2 days ago
add a comment |
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TruncatedIcosahedron is a new contributor. Be nice, and check out our Code of Conduct.
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Mathematica (Wolfram language) is great at this. You can set up a trial online account if you're just looking to do a handful of things.
– Kelly Lowder
2 days ago