Linked Questions
51 questions linked to/from Can I simplify an expression into form which uses my own definitions?
2
votes
2
answers
4k
views
Rewriting one expression using a variable representing another expression [duplicate]
I have two expressions:
w1 = (a+b)/c^2;
w2 = (a^3 + 3 a^2 b + 3 a b^2 + b^3)/c^6;
How can I ask Mathematica to try to find an alternative expression for ...
- 23
4
votes
3
answers
183
views
Rule can not work? [duplicate]
For example I have this equation,I want to use c->a/b ,but it can not work
$$
\frac{a^2}{b^2}+\frac{b^2}{a^2}+\frac{a}{b}+e^{a/b}+\frac{b}{a}+\log \left(\frac{a}{b}\right)
$$
...
- 1,562
0
votes
1
answer
3k
views
How to write a variable in terms of the other [duplicate]
I have an equation that defines a variable like y=4x+a. I had another equation, z=x+2+4, I would like to know if there is a way in Mathematica to get an expression in which z= a*y+C, in which a and C ...
- 1
2
votes
2
answers
401
views
Rewriting the set of equations in terms of new variables, using replacement rules when the expression contains partial derivatives [duplicate]
I am working with cumbersome equations, that contain a lot of terms. Here I will consider simple example:
...
- 607
3
votes
1
answer
185
views
ReplaceAll with Powers [duplicate]
If I run the following code:
a^2/b^2 /. {a/b -> c}
I'm getting output:
a^2/b^2
How can I obtain ...
- 33
0
votes
2
answers
808
views
Replacing a expression in another expression with a Variable [duplicate]
I want to set a symbol (or variable) for an expression. Here is an example:
A x^2 + C x + D
I want to reduce this expression to
...
- 1
3
votes
2
answers
197
views
How can I use ReplaceRepeated (//.) in this case? [duplicate]
Consider the following case:
(a^3*b) //. {a^2 -> c, a*b -> d}
instead of c d the output is:
...
- 6,687
1
vote
1
answer
158
views
Reverse substitution [duplicate]
If you apply rules and then simplify you may get something like.
(25 A^2 hbar Sqrt[π])/Sqrt[hbar m w]
How would you get mathematica to rewrite this in terms of E ...
- 881
2
votes
1
answer
312
views
How can I simplify the result of a differential equation by using my own defined expressions? [duplicate]
I want to solve the following differential equation with mathematica:
α β * w''''''[ξ] +
( 1 + α - p ) * w''''[ξ] + p/β * w''[ξ] = 0
The answer seems at ...
- 45
0
votes
3
answers
56
views
How to replace polynomials numerically? [duplicate]
We know that the value of this equation is 0
x2 y1 - x1 y2 == 0
For the following equation, there is a correlation between the polynomial parts of the known ...
- 4,051
1
vote
0
answers
149
views
Introducing new variables implicitly [duplicate]
I have a calculation
expr111 = cs[giso, xiso, 1, 1, 1]
that gives the result
-((k x)/(2 (1 + 1/4 k (x^2 + y^2 + z^2))))
I ...
- 11
1
vote
2
answers
114
views
How do I format expressions so that replacement rules correctly apply to exponents? [duplicate]
I have a series of rules that I would like to apply to a series of expressions with variables, but cannot get Mathematica to correctly recognize that these rules should apply when my variables have ...
- 11
1
vote
1
answer
113
views
Solving for a constant multiplier of a variable [duplicate]
I would like to make this manipulation:
Solve[r Sin[α[t]] + l Cos[ϕ[t]] Sin[γ[t]] == 0, l*Cos[ϕ[t]]]
But it seems that the ...
- 1,099
0
votes
1
answer
103
views
Substitution inside an expression [duplicate]
I'm trying to get mathematica to replace an expression with a reduced form. I wanted to replace $(k/w)$ with $h$ in a particular expression, and I've tried something like:
...
- 877
0
votes
0
answers
66
views
Simplify symbolic expression in terms of constants [duplicate]
Say I have an expression $a+b+a\times b$ and I define $c:= a\times b$. How do I get Mathematica to write $a+b+a\times b$ in terms of $c$, i.e. $a+b+c$?
- 1,273
0
votes
1
answer
48
views
Reducing Output length by introducing new variables [duplicate]
I have outputs like "expression/(1+3*c^2) +anotherexpression/(1+3*c^2)" and so on.
Is there any way to set 1/(1+3*c^2)=A where A is a new variable so that the output reads like "A*expression+A*...
- 1
1
vote
0
answers
39
views
replacement rules don't account for signs [duplicate]
I would like to make a single replacement rule that disregards the sign. I have the following expression:
...
0
votes
0
answers
32
views
Algebraic substitutions not working? [duplicate]
I have been trying to simplify this matrix
$$
\left(
\begin{array}{cc}
\frac{1}{2} \left(-2 g \sqrt{1-\text{tauA}} \sqrt{1-\text{tauB}}+\text{mu} \text{tauA}+\text{mu} \text{tauB}+\text{...
32
votes
6
answers
20k
views
Replacing composite variables by a single variable
To replace a single variable by another variable, one can simply use the the replace all (/.) operator (e.g., ...
- 1,397
22
votes
7
answers
19k
views
How do I replace a variable in a polynomial?
How do I substitue z^2->x in the following polynomial z^4+z^2+4?
z^4+z^2+4 /. z^2->x
...
- 2,623
32
votes
3
answers
3k
views
Common subexpression from two expressions
I am working with some unpleasantly tedious polynomials, which need to be manipulated in various ways (integrate with respect to some variable, differentiate with respect to another). Since these ...
- 421
16
votes
2
answers
3k
views
Is there a way to to substitute for symbols, simplify, and back-substitute?
In papers in physics and mathematics one often encounters longer mathematical expressions which have to be, for intuition and typesetting, expressed using symbols standing for recurring patterns in ...
- 415
16
votes
3
answers
2k
views
Find subexpression to minimize leafcount after replacment with temporary variable
Given an expression expr, is there an automated way to find a subexpression subexpr such that replacing ...
- 484
9
votes
3
answers
3k
views
Replace expressions with symbols
First of all: I'm new to Mathematica, so I would appreciate it if the answers are quite complete.
I have the result of calculation that is expressed in $\sin$ and $\cos$. Now, all of these can be ...
- 983
10
votes
3
answers
510
views
Matching (y/x)^u terms wherever the appear in an expression
Mathematica keeps rewriting expressions, so it is hard to figure what pattern to use.
I am trying to replace all occurrences of $\frac{y}{x}$ by $t$, but Mathematica re-writes $\frac{1}{\left(\frac{y}...
- 143k
6
votes
1
answer
1k
views
Reduce an equation by putting a new variable
I have the following equation given:
$$ (26-x)\cdot\sqrt{5x-1} -(13x+14)\cdot\sqrt{5-2x} + 12\sqrt{(5x-1)\cdot(5-2x) }= 18x+32. $$
In order to solve it, I want to substitute $t = \sqrt{5x - 1}-\sqrt{...
- 4,503
1
vote
1
answer
5k
views
Express in terms of a new variable [closed]
I have a simple expression:
s=4a(x+y)^3
I want to express s in terms of b where b=x+y. That is s will become 4ab^3. How to achieve this in Mathematica?
- 11
2
votes
3
answers
514
views
Question on alternate forms of polynomial output
EDIT: Would it be possible to do something like let $y=ax+b$ then use Collect[] or Apart[] on the new expression? How would I go about this. I've tried using Collect[%,ax+b], Collect[%,{ax+b}], and ...
- 275
3
votes
3
answers
640
views
Replacing a sum of expressions
I have an equation which Mathematica solves but gives a huge output. However I notice in this output that the same expression occurs many times. Namely:
$E=864 a^6 - 432 a^4 b^2 + 54 a^2 b^4 - b^6 + ...
- 147
2
votes
1
answer
1k
views
How to transform an expression using algebraical instead of pattern rules [duplicate]
I would like to transform rules algebraically. A very simple example would be: -
k^2 - 2 k x + x^2 /. {2*k -> 1}
This transforms to: -
$$k^2-2 k x+x^2$$
...
- 473
3
votes
1
answer
434
views
Collecting factors of polynomials
First up, I'm new to Mathematica and MathematicaSE, so please correct me if I'm doing anything wrong.
My problem is the following: I have a bunch of complicated polynomials in $3$ variables $x_1,x_2,...
- 155
2
votes
2
answers
115
views
Force using function definitions when simplifying
So, I have my function, such as
f[x_,y_]:=(1-x/y)^(1/2);
This function enters a big expression that contains variables x and y, as well as the function f. Now I ...
- 121
1
vote
4
answers
399
views
Replace a sum of squared variables by a new variable squared
Is there any way to tell Mathematica to replace $\kappa^2 + k_z^2 \rightarrow k^2$ in an expression? I want to make a result more readable, e.g. something like this:
$$\frac{2 k_z^3 \sqrt{k_z^2 + \...
- 191
0
votes
3
answers
441
views
How to simplify an expression by substitution?
Sometime Solve and DSolve give a finial form of the solution, which is fine in may applications. However, in some cases, one may ...
- 1,229
2
votes
1
answer
418
views
How to Collect $x$ powers to group $\sqrt{x}$ and $\sqrt{1+x}$ together?
I have been failing to apply Collect[#, x]& to render a like-power series of $x^k$. Here $k = \frac52, \frac32, \frac12,\frac{-1}2$, etc.
The major issue is:
...
2
votes
1
answer
386
views
Substituting variables inside a matrix
I'm trying to substitute some dependent variables into equations inside of a matrix, however $Replace[]$ and and $/.$ don't seem to work.
The equation in question is just a vector matrix of ...
- 105
1
vote
1
answer
475
views
Writing a trigonometric expression in terms of another [duplicate]
This is related to another question, in which one wants to rewrite a function of a single variable in terms of another function of that variable. Here I have a function of multiple variables. I want ...
- 183
1
vote
2
answers
167
views
How to "reversely" replace definitions?
I have the following problem at hand.
1.) I have a list of definitions like
...
1
vote
3
answers
202
views
Substitution in expressions
As the title suggests, I want in an expression to to some substitutions. For example in the expression $\mathcal{L}^+_0+\mathcal{L}^-_0+\mathcal{L}^+_0+\mathcal{L}^-_0+\mathcal{L}_1$ I want to ...
- 783
1
vote
0
answers
233
views
How to simplify expressions
I read several similar posts but I have not found a solution yet. However, I think that my problem should be quite easy. So here we are.
Relations
...
- 8,760
3
votes
1
answer
140
views
Replacing patterns (determinants) in a rational multivariate function and/or getting `replacementFunction` to work on a multi-linear expression
Given a rational multivariate function known to contain determinants, what is the best way to rewrite the function in terms of the determinants?
A simple example:
...
- 687
1
vote
2
answers
99
views
Applying a simple transformation rule when Plus automatically simplifies
I have the following simple rules:
{x2-x1->s1,
-(x2-x1)->-s1,
x3-x2->s2,
-(x3-x2)->-s2}
I want to apply that rule to the following:
...
- 25
3
votes
2
answers
96
views
Treat 2 variable as 1
Is there anyway to treat two variable, that are a result of expansion, as one?
To use Solve[] I can do
...
1
vote
0
answers
142
views
How to Pattern Match complicated patterns? [closed]
How can I get the output expressed in terms of p1 and p2 instead of exponentials?
...
- 4,602
1
vote
0
answers
131
views
How does PacletInstall work? And is it possible to find packages using PacletInstall?
It seems that many packages published could be installed using PacletInstall
. For example, from this Rubi install instruction webpage, we could see the comman:
...
- 165
1
vote
1
answer
58
views
How to simplify expression depending on former definition?
If
a = x + y
b = x - y
u = a + b
v = a
This gives me for u/v the expression (2 x)/(x + y)...
- 2,728
2
votes
1
answer
53
views
Replace subexpression that appears as inverse too
I have
eq=Sqrt[(g m)/h] Tanh[Sqrt[h/(g m)] t]
then I am trying to replace Sqrt[m g/h] by a symbol ...
user29726
0
votes
0
answers
84
views
Assign a variable to an expression in Mathematica
I have the following matrix
{{a^2 + b + \[Sqrt](m + n) + 5, 23 x + 7 a}, {14 b,
a^2 + b + \[Sqrt](m - n) + 5}}
I want to replace the expressions ...
- 663
0
votes
1
answer
79
views
Is there a way to use identities in Mathematica efficiently? [duplicate]
Imagine I have defined a variable
l=p/(a*b)
Let's say I perform some operations, and I get the final answer to be p/a.
But all I ...
- 101
0
votes
0
answers
72
views
Problem with replacing products involving identical variables due to the rewrite to powrs
This is most easily explained with an example:
Say I have a b^2 or a b a and I want to replace ...
- 4,419