Questions tagged [expression-manipulation]
How to manipulate expressions structurally, not necessarily complying with the rules of algebra.
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Symbolic PDE manipulation
I'd like to transform a PDE in a way such that I can express a temporal derivative as a spatial derivative using some known relation.
Very simple example:
...
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Confusing abnormalities observed when counting a specific operator in an expression [duplicate]
Recently I have met with some confusing abnormalities when trying to determine if there is a specific operator (usually Plus[] ) in an expression by programming. ...
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Extracting the constant term
Finite difference problem
There are a large number of variables, interacting at most five at a time. A sample term is:
How to extract the constant term?
In this example, the constant term is -1/4.
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Factorize expression by specific term [closed]
I am new to Mathematica but I would like to know how to force Mathematica to factorize an expression by a specific term.
Exemple, imagine I have a term like this:
And I have an expression like this:
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Can one collect with respect to two groups of variables?
Here is a toy example of what I want: given
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How to extract logarithmic terms in an expression?
I have some expressions of the type
$f(x) \,+\, g(x) \,\log(x) \,+\, h(x) \,\log(1-x^2)$
where $f$, $g$, and $h$ can be any rational functions of $x$. I am trying to use Mathematica to extract each ...
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Get rid of some solutions proposed by Reduce/Solve
I would like to take the result of a Reduce function call and eliminate any solutions that depend on the value of a particular variable (call it $y$). For instance, I am trying to get the parameters ...
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How do I extract the component from an expression
I'm embarrassed that I don't even know the language for what I'm asking. The result of an operation I'm performing is:
$$expression=-dt^2 \left(c + a t\right)^2$$
$dt$ is basically an infinitesimal in ...
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Speclevel in Reverse
I have an expression involving several dot products, I give a simplified example:
expr={A.B,C.D}
I want to reverse all dot products, and try
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Separating terms in an expression with many variables by their "nature"
I have an expression like this:
$f=t_1(\sin(\alpha),\cos(\beta),\cos(\gamma)^2) \cdot r_1(x,y,z)+t_n(\sin(\alpha),\cos(\beta),\cos(\gamma)^2) \cdot r_n(x,y,z)$
Where $t_i$ and $r_i$ - functions of ...
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Can Mathematica simplify expressions with prescribed relations?
I have a linear map $T$ on a vector space which satisfies $T^4 = 1$ and want to simplify expressions of the form:
$$[X,TY] + [Y,TX] + [Y,T[TX,TY]] + [X,T[TX,TY]],$$
where $[\cdot, \cdot]$ denotes the ...
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How to use RightComposition efficiently in the context of one-liners?
I find myself recently writting, more often than not, code that makes heavy use of RightComposition eg.
expr//f/*g/*h
It is relatively straightforward to first ...
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How to convert Graph atomic object back into unevaluated expression? [duplicate]
For the purposes of further development of my shortInputForm function, I wish to convert Atomic objects such as Graph into non-...
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Extract first term of each element in a list
Suppose I have a list of the form
list={a+b,c+d,Xi+Psi*Zeta,0}
How can I make a list of only the first term of each element in that list? In this case the list ...
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How to convert this Mathematica expression to another, as described here?
I am working on a function of which the core will consist of something like:
...
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Get depth of vertices in TreeGraph
I want to get the depth of each vertex in a TreeGraph, g. I might convert g into an ...
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Encode expression into a list
I have an expression of the form:
$$c {\partial^{k+l} \Phi(\theta,\phi,n) \over \partial \theta^k \partial \phi^l}$$
$n,k,l$ are (positive) integers. $c$ is some constant. It is also possible that $c$ ...
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Converting an indefinite integral to definite integral
For example, I have the following integral expression:
g[x, y] = Integrate[f[x, y],x]
How can I modify the above expression to achieve the following definite ...
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Factoring an arbitrary power from the rest of the expression in an exponential expression
I have the following expression:
Exp[r*t*x + e*r*y + t*x*r^2 + y^2*e*Sqrt[r]]
I want to choose some arbitrary terms in the power and for example write the ...
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Simplifying multiplies of sums into a single double sum
I have the following expression:
Sum[x^n, {n, 1, Infinity}]*Sum[Log[m, x], {m, 2, Infinity}]
How can I Force Mathematica to write this expression in the following ...
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Transforming one exponential expression to multiplication of exponential expressions [duplicate]
I have the following expression:
Exp[a * x + b * y + c * z]
I want to write this expression as:
...
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How to express Bessel Functions in terms of Hankel Functions
I have the following expression
BesselJ[\[ImaginaryI]*m, k*r]
FunctionExpand knows how to transform from ...
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How can I extract a list of terms with functions in terms of a specific variable
I have an expression in the following form:
a f[x] + b Exp[g[x, y]] + r[z] f[y] + f[y] Sin[h[x, y, z]^2] + r[z] Log[t[z, y]]
I want to extract an expression ...
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Same displayed expressions produce different outputs
I know EngineeringForm is a wrapper which prevents evaluation of content, but pasting chunks of other cells with an EngineeringForm number, got these two simple expressions w/ the same input ...
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How to make a function in terms of constants to inherit the attribute of being constant
I have defined two variables a and b:
SetAttributes[a, Constant];
SetAtributes[b, Constant];
I have defined a function c as ...
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Extracting expressions from LHS of an assignment
I need to list all variables in a notebook containing several Set assignments, lhs=rhs, and equations, ...
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Equality of expressions with different variable names
I have some multivariate systems of expressions that I want to check for equality up to allowing relabelling of the variables. For example the two expressions below would be the same:
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Coefficient works on $\pi$, $x$ and $x^2$, but not on $\pi ^2$
Consider
(\[Pi] + 2 \[Pi]^2 + 3 x + 4 x^2)
Executing
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Manipulation of expression
Let
ss2 = (γ + ν)/β;
is2 = ((γ + ν)/β) (β/((γ + ν)) - 1);
I wish to do the following computation but want to keep the output in terms of ss2 and is2:
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Simplify radical expression (a + b - Sqrt[a^2 - b^2])/Sqrt[a + b]
I have the following expansions:
$\frac{a+b-\sqrt{a^2-b^2}}{\sqrt{a+b}}$ and $a>b>0$
Obviously we can simplify it further by hand $\sqrt{a+b}-\sqrt{a-b}$, but Mathematica doesn't know how to ...
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Block Behavior, but for Function Assignment instead of Variable Assignment
We can define a function using a variable b that does not appear as an argument, and then using Block, change the output of the ...
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How i can move the slider Below X axis and beside Y axis of plot? [closed]
I want to place this slider below the x-axis and Vertically beside the y-axis.
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Cutting of terms on denominators of giant expression
I have an immense expression of the form
$$
\sum_i \frac{f_i(X,Y,x,y)}{(a_iX^2+b_iY^2+c_ix^2+d_iy^2)(e_iX^2+g_iY^2+h_ix^2+k_iy^2)},
$$
where at $a_i$ or $b_i$ AND $e_i$ or $g_i$ is different from zero....
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Can I specify which terms to show on the left side and which on the right side of an equality in output?
Mathematica unexpectedly moves a part of the result of the calculation to the left side where I want to display only the unknown variable.
Can I prevent this?
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Grouping together same exponent terms in a multivariate monomial
This is a rather simple question but for some reason, I am spending too much time on this.
Suppose I have a monomial in 4 variables, each raised to some linear combination of 3 exponent variables: <...
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Make Mathematica not to evaluate an integral?
I want the output to contain an integral, while everything under the integral sign evaluated. How can I prevent the system from evaluating the integral?
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Input output in Wolfram Cloud
This is a starter query. I know if I enter 2+2 and press enter, I get 4.
Similarly, I enter ...
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Manipulating an equation to isolate a term (not solve for a variable)
Consider the following minimal example of my problem:
eq = (a^2 + a == b^2)
I would like to manipulate this equation to achieve:
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Evaluate a function with 3 different variables for the whole list of each variable
I have a function with 3 variables
f[t1,t2,t3]
Each function has a list of values
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Decompose expression into specified form of partial fractions
In order to obtain the partial fractions of an expression, I used the function Apart to realize it. However the result is shown as Figure 1 which isn't what I want. ...
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Formal substitution of exponential factors in an expression
Assume that we have some complex algebraic expression, like
Exp[(a t + b s)/w] ( t Exp[ q t] w + q Exp[q s] Exp[-2 s] + a^2 Exp[3 s] + s t + 1 )
Now, this is just ...
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Pattern matching problems involving FullForm and Plus and Times [duplicate]
I am trying to match an expression that will be a sum of more than one terms, with the last one being a product. For example, the objecta+b+x*y. I am using the ...
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Issues in expanding expressions with formal sums
I have a very long expression involving formal sums to infinity, unfixed functions and several variables.
In this very long expression, I need a typical term, like
$\frac{6 A \sigma \sum _{n=0}^{\...
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How to rearrange terms in an expression to a particular form (e.g. A/w-> A*(1/w)
I have a huge expression for which the numerators are a big mess, involving numbers, variables, formal sums and unevaluted function, let's call the numerators Ai, with i=1,2,...n
This "beast"...
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How to extract a factor from equation and rearrange the equation?
I want to extract a factor from the equations, it's not a common factor, just a factor defined by myself, like this:
(ac+b) --> c(a+b/c)
I have tried Factor,<...
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Applying Operators inside complex expressions to argument with Through
I am developing some functions to help me work with Quantum Mechanics Momentum Operators. Here, for simplicity, I represent them with these simple functions because the actions of the operators ...
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Approximating giant polynomial expression
Suppose I have a giant polynomial expression analogous to
$$
F=a_1xX^6+a_2x^2X^5+a_3x^3X^4+a_4x^4X^3+a_5x^5X^2+a_6x^6X
$$
and it is true that $X \gg x$. Let it be enough for me to approximate this ...
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Converting a vector of expressions into functions with the index being an input
I am trying to generate a list of functions from a vector of expressions. I have the list
$H=[1,x,x^2+1,3x^3+2x,4x^2+2x]$ and I want to define a function $f$ using two inputs such that
$f(n,x)$ ...
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How to delete certain terms in a polynomial with variables in subscript?
I have a polynomial in the following style,
...
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