Questions tagged [assumptions]
Questions about the function Assuming[], the $Assumptions system variable, and the Assumptions option of functions such as Simplify[] and Integrate[].
517
questions
3
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1
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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
...
- 438
2
votes
2
answers
43
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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 ...
1
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0
answers
25
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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 ...
- 111
1
vote
0
answers
50
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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]
...
- 38.2k
0
votes
0
answers
58
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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 ...
- 1
0
votes
1
answer
53
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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 ...
1
vote
1
answer
114
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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 ...
1
vote
0
answers
47
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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{...
- 11
1
vote
0
answers
42
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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 ...
- 159
0
votes
0
answers
63
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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 ...
- 153
4
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2
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181
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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.)
...
- 159
1
vote
0
answers
34
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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 ...
- 753
0
votes
0
answers
32
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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 ...
- 23
4
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1
answer
84
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1
vote
0
answers
35
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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
...
- 593
0
votes
1
answer
61
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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 $r_s< r$ ...
- 438
2
votes
1
answer
110
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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).
...
- 273
0
votes
1
answer
66
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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 ...
- 1,159
0
votes
1
answer
52
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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 ...
- 137
0
votes
0
answers
30
views
Assuming a variable arbitrarily close to a value in Refine
In my assumptions, I want Mathematica to use the fact that Theta is arbitrarily close to $\pi$ from below. I made this assumption :
...
- 496
3
votes
1
answer
61
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0
votes
0
answers
30
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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...
- 1,212
2
votes
2
answers
85
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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 ...
- 471
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votes
1
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47
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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 ...
- 1
5
votes
3
answers
162
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$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 $Q^\dagger = Q$.
...
- 53
2
votes
1
answer
101
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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
...
- 415
0
votes
1
answer
75
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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 ...
- 165
6
votes
2
answers
184
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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
$$I = \int\limits_2^4 \frac{\sqrt{\log (9-x)}}{\sqrt{\log (9-x)}+\...
- 38.2k
8
votes
1
answer
223
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Why Mathematica is treating the product of (specified) real variable as complex?
For the given matrix
...
- 539
4
votes
1
answer
52
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Proper usage of Assuming statement
I want to evaluate a command under an assumption, and thought Assuming was the right way to go. Suppose we want to calculate a Matrix rank. Following the second ...
- 251
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0
answers
30
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Put an initial condition on some parameter
Good morning,
I'm new in the world of Mathematica, so I'm sorry if my question isn't very relevant.
I'm trying to solve a system of 5 equations withs many parameters. To be clear, I will hit the core ...
- 101
5
votes
2
answers
122
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Simplifying expressions with nested square roots
When I run
FullSimplify[Sqrt[(1 - Sqrt[1 - 2 x^2 y^2])^2], {1 > 2 x^2 y^2 > 0}]
I obtain 1 - Sqrt[1 - 2 x^2 y^2]. However,...
- 395
2
votes
2
answers
135
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Why is my integral with the error function not being evaluated?
I'm new to Wolfram Mathematica and I was trying to evaluate this integral in particular:
$$\int_{0}^{x}\frac{e^t \operatorname{erf}(\sqrt{t})\sqrt{\pi t}+1}{\sqrt{\pi t x -\pi t^2}}\mathrm dt$$
The ...
2
votes
1
answer
109
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Integrate ignoring assumptions
I want to evaluate an integral with all variables real and positive. Specifically,
...
- 339
1
vote
2
answers
150
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Argument of a complex number with assumptions
I am trying to calculate the argument of a complex number:
Arg[Cos[y]*Exp[I x]]
where both x and y are real. The solution is clearly x, but I can't get it with ...
- 51
4
votes
2
answers
113
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Simplify with False assumptions gives wrong answers
Simplify is very gullible: if it gets a False assumption, it'll believe anything is True:
<...
- 19k
6
votes
3
answers
141
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Extracting a logarithmic divergence of an expression using Series
Consider the following expression:
...
- 1,317
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vote
1
answer
33
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Getting the same result from Integrate as Probability
I'm trying to solve a Baysian inference problem (although the details are not all that important for this question)
I define two probability distributions P and <...
- 819
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votes
2
answers
50
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`Assuming` combined with mathematical notation of `Integrate`
I am trying to write down the following expression
Integrate[Exp[-a/2/x]/x/(x + 1), {x, 0, b}, Assumptions -> a > 0 && b > 0]
using mathematical ...
- 1
0
votes
0
answers
39
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Integer parameter assumption gives incorrect result when integrating
There are some dangerous pitfalls that can happen when evaluating some integrals, assuming that some parameters are integers. For example, consider the following:
...
- 1,317
0
votes
2
answers
134
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Assumptions in Integration for positive real values [closed]
I want to evaluate the following integral in Mathematica.
$$ \int_0^\infty \frac{a^{-t}-b^{-t}}{t} dt = \ln \left(\frac{\ln b}{\ln a} \right)$$
I try to enter this, but Mathematica can't figure it out....
- 1
1
vote
0
answers
39
views
How to declare at the beginning of the notebook that a variable belongs to a set?
In the notebook I am working on I have certain symbolic variables (e.g., c and r) which I would like to declare since the very first few lines to be non negative real numbers. Correct me if I am wrong ...
- 53
2
votes
1
answer
61
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How to use System`Private`AssumptionAccess and Assumptions`*?
I see this function is used by some symbols in Assumptions`*, and it HasDownCode and does not ...
- 3,630
3
votes
1
answer
278
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Mathematica tries to differentiate Abs[x] and this causes a problem? [duplicate]
I am trying to run the following code:
...
- 5,061
0
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0
answers
72
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Global assumption non zero
I would like to define globally an assumption stating that I have a nonzero real vector $v$.
For now, I put :
$Assumptions = Element[v,Vectors[{100},Reals]]
but $v$ ...
- 496
2
votes
1
answer
83
views
Simplifying an expression with complex conjugates
I have been unable to do the following. First I make an assumption $Assumptions = x \[Element] Reals; and define ...
- 79
1
vote
1
answer
59
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Why does not ContourPlot consider the condition given in RegionFunction in the given code?
I have two functions $f(x,y)$ and $g(x,y)$. I am using RegionFunction in ContourPlot to see those values of $(x,y)$ for which $...
- 659
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2
answers
108
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4
votes
2
answers
409
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How to get a manipulated plot of the intersection points of two curves without finding them numerically?
I have four 2-variables functions for $0<x<3$ and $1<y<3$
...
- 659
2
votes
1
answer
68
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Identical integral evaluating differently
I am trying to compute an integral but am getting two different answers using two near-identical methods. I wish to know why they differ.
...
- 21