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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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 ...
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5 votes
3 answers
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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 $Q^\dagger = Q$. ...
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1 answer
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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 ...
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1 answer
50 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 ...
6 votes
2 answers
174 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)}+\...
8 votes
1 answer
219 views

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

For the given matrix ...
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4 votes
1 answer
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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 ...
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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 ...
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5 votes
2 answers
101 views

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,...
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2 answers
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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
95 views

Integrate ignoring assumptions

I want to evaluate an integral with all variables real and positive. Specifically, ...
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1 vote
2 answers
103 views

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 ...
4 votes
2 answers
103 views

Simplify with False assumptions gives wrong answers

Simplify is very gullible: if it gets a False assumption, it'll believe anything is True: <...
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6 votes
3 answers
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Extracting a logarithmic divergence of an expression using Series

Consider the following expression: ...
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1 answer
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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 <...
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2 answers
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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 ...
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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: ...
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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 vote
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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 ...
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1 answer
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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 ...
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1 answer
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Mathematica tries to differentiate Abs[x] and this causes a problem? [duplicate]

I am trying to run the following code: ...
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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 $v$ ...
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1 answer
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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 ...
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1 vote
1 answer
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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 $...
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2 votes
2 answers
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Is it possible to exclude a condition, say, $f(x,y)=const.$, from a ContourPlot code?

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2 answers
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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 $1<y<3$ ...
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2 votes
1 answer
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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. ...
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1 answer
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Adding Assumptions in double integral written in "math input" mode

I've the following double integral and I'd like to write Assumptions->Re[c]>0, but if I try to do it, I get a syntax error. How can I add the above condition but without changing the ...
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How to make assertions for subscripted variables?

I'm trying to write a formula using subscripted variables like x₁, x₂, x₃, ..., so that I can later retrieve their values programmatically. However, I'm struggling ...
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The derivation and simplification of the functions HeavisideTheta and Dirac

I encounter some problems, can you help me? Thanks. Step (1) gives the expected result 3 DiracDelta[x], why (2) and (3) can not give expected result ...
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Can I use assumptions to declare a variable's type?

I'm trying to declare $P$ as a vector. I searched for a while, the closest way seems to be Assumptions: ...
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2 answers
49 views

How to assume some variables to "not" be a function of other variables at the time of defining a function [closed]

I have a function with the following definition: F[x]=Exp[q*w*x]; I want to take total derivatives of F. How can I define that q and w are not dependent on x at the ...
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Simplify expression with assumption that all variables are real

I have an expression in which all variables are real. However when I simplify the expression with appropriate assumptions a 'Conjugate' still remains. How can I get rid of this? Here is my code ...
2 votes
0 answers
104 views

Why does this ConditionalExpression appear? [closed]

I am new to Mathematica. Could anyone help explain why ws > 0 appears in the solution? How to define symbolic variables' range? Thanks! EDIT to include code <...
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2 answers
100 views

How to solve system of equations with complex variables

I'm trying to obtain the solution to the following system of 3 equations and 4 variables: ...
1 vote
1 answer
78 views

How to 'define' value in Assumptions but not let Simplify replace it? [closed]

I want to let Simplify know the exact value of a symbol, to resolve logical statements, but don't want it to actually replace it. For instance, I would like ...
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1 answer
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Get Real Solutions works in Solve but PositiveReals don't (Quantities)

I'm trying to get the R+ Solutions to a school problem with solve. Everything works fine with Dom -> Reals but when I try ...
2 votes
0 answers
67 views

Defining new Domain for variables

I am trying to define a new Domain for variables to use with functions like FindInstance or Solve. For example, If I wanted to solve x+y+z=1 over the Reals, I'd get a large solution space. But If I ...
1 vote
0 answers
50 views

TensorExpand ignores assumptions?

Here's a minimal example to demonstrate my problem: ...
1 vote
1 answer
82 views

Simplify an expression with assumptions connected with OR

Mathematica doesn't seem to have any problem with these commands: ...
4 votes
1 answer
250 views

Why isn't this expression returning true to being positive when it is clearly positive?

Consider: ...
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Test domain assumption of a variable

Using $Assumptions to define the domain of variable is straightforward, i.e. $Assumptions = Element[x, Reals]. Nevertheless, it'...
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4 votes
1 answer
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Representing number domain by a symbol [closed]

I'd like to represent the number domain by a symbol rather than text word. While Solve[n^2 - 19 n + 99 == k^2 \[And] {k, n} > 0, {k, n}, Integers] works fine, I'...
4 votes
3 answers
1k views

How can I specify the assumption 'a' is much greater than 'b' (a>>b) in Mathematica?

I want to evaluate an expression of type 1/(r-2 m), assuming r >> 2 m. This is regarding black hole physics and r = 2 m is the Schwarzschild radius. But I am working on something where I need to ...
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1 vote
0 answers
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Piecewise and Assumptions [closed]

Assumptions sometimes work as expected with Piecewise, for example Simplify[Piecewise[{{A, a + b >= c}, {B, True}}], Assumptions -> a + b > c] correctly ...
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1 vote
1 answer
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Solving generating conditional expression despite assumptions

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2 answers
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Triple integral: How do I include assumptions and conditions?

I would like to solve the following integral: $$I=\int_{0}^{a} \int_{0}^{y} \int_{0}^{z} e^{(a-x)^{3}} d x d z d y$$ with the condition that: $$a>0$$ So I tried to input the equation like below ...
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5 votes
2 answers
208 views

Why Mathematica is not assuming real variable as real?

I am dealing with the situation where despite of specifying my variables b1 and c to be greater than zero, Mathematica still ...
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1 answer
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how can I modify this function to convert to polar form for any complex expression?

The function from another post is to convert a complex number to polar form. polarForm = Expand[# /. z_?NumericQ :> Abs[z] Exp[I Arg[z]]] & Now if I apply ...
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1 vote
1 answer
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How to generate assumptions automatically for definite integrals?

In Mathematica, a trick to speed up the process of definite integrals is by adding assumptions. For example, the following codes run faster if we add such assumptions: ...
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