Questions tagged [assumptions]

Questions about the function Assuming[], the $Assumptions system variable, and the Assumptions option of functions such as Simplify[] and Integrate[].

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How to assume a function is holomorphic?

For example, for a holomorphic function $f(z)=f(x,y)$, it's well know that $\ln |f|$ is harmonic. I want to check it with mathematica with the following code: ...
gaoqiang's user avatar
1 vote
3 answers
101 views

Why does assuming f[_] > 0 does not work while Element[f[_], Reals] does?

Refine works with symbols in either way: Refine[Sqrt[x^2], Element[x, Reals]] (* Abs[x] *) Refine[Sqrt[x^2], x > 0] (* x *) ...
JS S's user avatar
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Simplify vector calculus based on component splitting

I am interested in verifying a few Vector Calculus expressions using Mathematica. These expressions are based on splitting a vector field into its transverse components (in the xy- plane) and ...
orlandini's user avatar
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98 views

Integral of complex exponential with assumptions

I feel confident this problem has been posed before but alas I cannot find it. ...
David G. Stork's user avatar
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2 answers
51 views

Can a redundant condition be removed from a solution?

A solution to this equation: Solve[{(p-x)^2 + (q-y)^2==d, p/q==t}, {p,q}, Reals] has this repetitive condition: $\displaystyle\quad d > \frac{x^2 - 2txy+t^2y^2}{...
scriptfoo's user avatar
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Assuming Refine does not work for all If[] expression part

One simple example as following ...
eason's user avatar
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0 answers
63 views

Solving multiple inequalities

I am new to Mathematica and I want to know if there are solutions to the following 4 coupled inequalities. Note that the inequalities are long and cumbersome with many variables with subscripts (I ...
Monty's user avatar
  • 101
2 votes
2 answers
97 views

Computing a limit with assumptions

This program solves the recurrence for the expected time to extinction of a linear birth and death process with arrival rate A and death rate q A, and then attempts to simplify. ...
florin's user avatar
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4 votes
1 answer
119 views

Questioning Mathematica's Condition Representation: Strange Solution for Integer Variable

I have the following sequence: $$f_n(x)=\left\{\begin{array}{cl} 1 & \text { if } 0 \leq x<\frac{1}{2} \\ 1-(n+1)\left(x-\frac{1}{2}\right) & \text { if } \frac{1}{2} \leq x<\frac{1}{2}+\...
Mark's user avatar
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4 votes
2 answers
118 views

Why $\texttt{Sqrt}[\textrm{positive value}] > 0$ sometimes simplifies to true, sometimes not

Why this does not evaluate to True: ...
scriptfoo's user avatar
  • 201
2 votes
1 answer
127 views

"Assume whatever makes it easier" command

Is there a shorthand for telling Mathematica to assume things like "everything is a positive real unless specified otherwise" etc? It get's really tedious for expressions with many ...
Gappy Hilmore's user avatar
2 votes
2 answers
93 views

Assumptions in Sum

I am calculating the following ...
mattiav27's user avatar
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2 votes
1 answer
143 views

Evaluation of integral with parameters

I am trying to solve the following integral having two strictly positive parameters: ...
cpcf's user avatar
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1 vote
1 answer
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Redundant cases from Sum

I am new to Mathematica. I would like to understand why Mathematica returns redundant cases, and whether it is possible to simplify them to the generic case $(n>1)$ that covers everything $(n\ge0)$....
Andras Vanyolos's user avatar
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0 answers
47 views

Simplify a ComplexExpand with assumptions gives wrong output

Let us define the real and imaginary parts of a specific polynomial root as follows ...
annuk89's user avatar
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0 answers
19 views

Specifying and assigning arguments of a function to be real

I have the following complex matrix that I wish to integrate (element-by-element) ...
kowalski's user avatar
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5 votes
3 answers
116 views

Implementing symmetry assumptions in FullSimplify

I want to symmetrise a long expression, M, that involves a function of 4 arguments, f[u1,u2,d1,d2], and its products (for ...
jms547's user avatar
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1 answer
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A problem with the evaluation of expressions using assumptions through Mathematica

I want to evaluate the expression below, $((2 (a_{01}+2 ya_{02}+x a_{11})^2+(b_{01}+2 y b_{02}+x b_{11})^2) (2 (a_{10}+y a_{11}+2 x a_{20})^2+(b_{10}+y b_{11}+2 x b_{20})^2))$, at $x=-((2 (2 a_{02}a_{...
VH84's user avatar
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1 answer
46 views

Assisting Solve to generate solution to a complicated equation

I have the following Mathematica code: ...
codebpr's user avatar
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1 vote
1 answer
101 views

FunctionPoles with arbitrary undefined function

Good day everyone. I have very simple question about behaviour of the functions FunctionPoles, FunctionMeromorphic e.t.c. Can these functions work properly with undefined functions? For example when I ...
George's user avatar
  • 69
3 votes
1 answer
88 views

Assume asymptotic value in a limit?

Is it possible to give Mathematica a limit about's function at infinity? For example I would like to ...
Nitaa a's user avatar
  • 698
2 votes
2 answers
50 views

Subtituting kronecker deltas for products in simplification

I have a problem where I have some vector, $a = (a_1, a_2, \ldots, a_n)^T$ that I want to have a Kronecker delta multiplication rule, $a[i]a[j] = \delta_{ij}$ (these are basically basis vectors, but ...
Joshua Schraiber's user avatar
1 vote
0 answers
27 views

Making an "unsafe" simplify that ignores the validity conditions of simplifications

Mathematica will never make assumptions you don't tell it to make, and will state all conditions under which the answers it gives are valid. While this is overall a good thing, this often leads to ...
eyeballfrog's user avatar
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92 views

Compute symbolic identities for FourierTransform

Mathematica computes some of the identities for Fourier transforms for an arbitrary function f[t] directly, for example: FourierTransform[f'[t], t, w] ...
David G. Stork's user avatar
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0 answers
62 views

Refine not able to simplify for PositiveReals

If I type in Mathematica Refine[d^2 == a^2, {a ∈ PositiveReals, d ∈ PositiveReals}] I get d^2 == a^2 Why don't I get ...
Kelthar's user avatar
0 votes
1 answer
84 views

How to tell Mathematica to solve an equation assuming all solutions are non-negative reals? [closed]

The title. I have a system of 6 equations that I want to solve. The system is non-linear. I want to solve it, but I just want Mathematica to give me solutions that are non-negative reals (so no ...
Granger Obliviate's user avatar
1 vote
1 answer
147 views

How can I force Mathematica to calculate this integral?

I have the following expression. I realize Mathematica has a little bit of trouble with Abs[] as it assumes variables to be complex and etc., but I am trying to compute an integral and it just keeps ...
Granger Obliviate's user avatar
1 vote
0 answers
56 views

Finding the (symbolic) eigenvalues of a matrix with some assumption

I have the following 3$\times$3 symmetric matrix with symbolic entries. Meff = \begin{array}{ccc} 2 \beta \text{c12}^2 \text{c13}^2 \text{$\eta $11} \text{m1}+\alpha \text{c13}^2 \text{D31} \text{...
neuoscman's user avatar
1 vote
0 answers
45 views

Enforcing the continuity of solutions throughout the whole range of variable in NDSolve, when there are multiple solutions

I am solving differential equations numerically by using NDSolve. Let's say that the function that I want to obtain is f[t]. Then, it turns out that my differential equation is a sextic polynomial of ...
Youngsub Yoon's user avatar
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0 answers
81 views

Why do I get different results for this complex line integral?

I want to compute line integral of $f(z) = \frac{1}{z(z-1)^{n+1}}$ over a closed curve $\gamma: t \mapsto 1 + \frac{1}{2} e^{i t}, t \in [0,2\pi]$ in the complex plane in two different ways but the ...
Physor's user avatar
  • 153
5 votes
2 answers
238 views

How can I make assumptions in NDSolve?

Suppose I try to solve the following differential equation numerically. (My example is much more complicated, but for simplicity, let's consider this example.) ...
Youngsub Yoon's user avatar
1 vote
0 answers
35 views

Is there a nice way to deal with sets in an abstract/symbolic way?

For instance, if I wanted to declare $A$ to be the set of all finite subsets of $\mathbb{Z}$, and declare $B$ to be a set comprising all finite subsets of $\mathbb{Z^{-}}$, and then declare $C$ to be ...
Trev's user avatar
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38 views

Double variable integration unable to prove that integration limits are real

I have simple question regarding double integrating a function. J*Integrate[Integrate[Cos[ArcTan[Sqrt[(x - a)^2 + (y - b)^2]/L]], {b, -b, b}], {a, -a,a}] The error ...
M. Dogan's user avatar
4 votes
1 answer
88 views

Simplify and Assumptions

Am I missing something here? Thanks for any help! SN
Sébastien Neukirch's user avatar
1 vote
0 answers
36 views

Limitations of Assumptions

Why don't Simplify[x[2, 1] < x[1, 3], Assumptions -> {x[a_, b_] > x[c_, d_] /; a > b && c < d}] or ...
user46831's user avatar
  • 633
0 votes
1 answer
64 views

Integral behaviour?

I'm trying to find a standard integral, which shows itself up in general relativity (proper distance in Schwarzschild metric). For example in this video. The integral is shown as where $r_s< r$ ...
Nitaa a's user avatar
  • 698
3 votes
1 answer
178 views

Why does the assuming not work as expected?

Why does this not work? I expect the output would be something like 1/s*e^-(sT). ...
internet's user avatar
  • 517
0 votes
1 answer
69 views

What is the most efficient/optimal way to simplify the given function? Does the given code need more assumptions?

I have a very long function for $\{x,b\}\in\mathbb{R}$ and $n=\{1,2,3,4,5,6,7,8,9,10\}$; here, I have only mentioned a short part of that. The function is a sum of the complex exponentials (a picture ...
charmin's user avatar
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0 votes
1 answer
53 views

How to use Assuming and With together

(I am sorry for the ASCII form, I use the free WolframEngine which works in text mode.) I have these assumptions ...
scriptfoo's user avatar
  • 201
3 votes
1 answer
69 views

Selecting the negative expression

Let Theta,t be real variables and Phi an expression of ...
Smilia's user avatar
  • 592
0 votes
0 answers
45 views

Mathematica FullSimplify becomes less simplified with more specific assumptions?

As far as I always understood, Mathematica always assumes an expression to represent the most general state. For example, a variable is usually assumed to be Complex...
infinitezero's user avatar
  • 1,357
2 votes
2 answers
100 views

Pattern or ForAll statment in Assumptions

I would like to simplify an expression like $\sum _{i=1}^k \sqrt{a_i^2}$, with the condition $\forall _{i\in \mathbb{Z}_{>\, 0}}a_i\in \mathbb{R}_{>\, 0}$ and with $k$ being undefined, which ...
Mammouth's user avatar
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0 votes
1 answer
47 views

Need help with Assumptions for an integral

I want to solve this Log, Integrate[2a Log[-a+((A0 + (y-y1)²)^½, {y1, 0,b}] But Mathematica only gives me long conditional expressions or imaginary numbers. I (my thinking which can be wrong) assume I ...
M S's user avatar
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5 votes
3 answers
204 views

$Assumptions = _ ∈ Reals results in incorrect simplification of ConjugateTranspose[..]

The linear combination $Q$ of two Hermitian matrices $A^\dagger = A, B^\dagger = B$ with real coefficients $m,n \in \mathbb{R}$, i.e. $Q = m A + n B$ is itself a Hermitian matrix $Q^\dagger = Q$. ...
qntdni's user avatar
  • 53
2 votes
1 answer
155 views

Struggling to get Solve to accept assumptions

I can't get Solve to solve the following two equations under the appropriate assumptions. When I enter ...
Bruce Bartlett's user avatar
0 votes
1 answer
162 views

Assuming one variable is greater than another variable

I want to add the assumption that M>m, but I am not sure how to do that. I tried Assuming[M > m, M > m] But this ...
bobsacameno's user avatar
6 votes
2 answers
190 views

Making a substitution within a typeset integral

This question derives directly from this one, but concerns instead a different matter... one related to display format. This integral $$I = \int\limits_2^4 \frac{\sqrt{\log (9-x)}}{\sqrt{\log (9-x)}+\...
David G. Stork's user avatar
8 votes
1 answer
226 views

Why Mathematica is treating the product of (specified) real variable as complex?

For the given matrix ...
seeker's user avatar
  • 539
4 votes
1 answer
54 views

Proper usage of Assuming statement

I want to evaluate a command under an assumption, and thought Assuming was the right way to go. Suppose we want to calculate a Matrix rank. Following the second ...
black's user avatar
  • 251
0 votes
0 answers
34 views

Put an initial condition on some parameter

Good morning, I'm new in the world of Mathematica, so I'm sorry if my question isn't very relevant. I'm trying to solve a system of 5 equations withs many parameters. To be clear, I will hit the core ...
A H's user avatar
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