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 tell Mathematica that certain variables are real/imaginary, integer-valued, etc
I'm trying to expedite some quantum mechanical calculations (expectation values etc.) by running them through Mathematica. When I say, for example,
...
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4
answers
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Usage of Assuming for Integration
For some reason, when I enter the following integration in Mathematica
Assuming[{k ∈ Integers}, Integrate[ Exp[ I k t], {t, -π, π}]]
the result turns out to be 0....
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votes
1
answer
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Are greek symbols causing different evaluation?
I've updated today to Mathematica 9.0.1.0 from version 8 and found something that absolutely confuses me.
Let us define a piecewise function:
...
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votes
4
answers
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An apparently "simple" limit?
Let $c$ and $h$ be real values.
I was using Mathematica to compute the limit $(h \rightarrow \infty)$ of the following expression:
$$
\frac{\left(h^2 +c^2 h^2 + \sqrt{4 h^2+\left(h^2+c^2 h^2\right)^2}...
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votes
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How to assume all variables in my code are reals
I won't have any occasion to have any imaginary number in my code. If there are any, that is an error.
So allowing the imaginary case simply hinders the equation manipulation and simplification.
I ...
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votes
2
answers
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Why doesn't FullSimplify drop the Re function from an expression known to be real?
For some reason Mathematica does not properly simplify this expression:
...
- 1,471
21
votes
2
answers
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Optimization with assumptions
I have the following problem, when I am trying to optimize function with pre-defined assumptions.
I am using Mathematica 8 and I wrote the following simple code
...
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20
votes
4
answers
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Complex number operations: telling Mathematica variables are real
I want to do Conjugate[a + b*I], but when I do that, the solution is
Conjugate[a] - I*Conjugate[b]; when for me, a and b are ...
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19
votes
3
answers
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Why does Mathematica simplify $x/x\to1$?
If I enter x/x, I get 1. Such behavior leads to this:
Simplify[D[Sqrt[x^2], x, x]]
0
...
- 7,182
17
votes
3
answers
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Logarithm of exponential [closed]
Ok, this is awkward.
E^Log[a]
gives a, which is what I expected, BUT,
Log[E^a]
is not ...
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16
votes
2
answers
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How to specify assumptions before evaluation?
If I request mathematica evaluate an integral for me, I'll often get a more general ConditionalExpression than I want. Example :
...
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16
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4
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Defining the domain of positive real numbers
I am trying to solve an equation by assuming that all the variables are real and strictly positive. I can use the keyword Reals for the argument ...
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votes
2
answers
634
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How to make use of NumericQ[x] = True (and use it safely)?
Basic Issue:
I'm trying to understand the proper use of NumericQ's "magical" capabilities. Please consider the examples below. Actual question and some links are ...
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votes
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answers
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Does $x>0$ imply that $x\in\mathbb{R}$?
Let’s assume I input
Assuming[x > 0, expression]
Is it assumed by Mathematica that $x$ is a real number? Or that the real part of $x$ is positive? Something ...
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15
votes
2
answers
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Behavior of Solve with $Assumptions changed in 12.2
Something changed with Solve between versions 12.1 and 12.2.
12.1:
...
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14
votes
3
answers
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Why does Integrate declare a convergent integral divergent?
When I try this command
Integrate[1/Sqrt[(s^2 - u)^2 - 1], {s, m, Infinity}, Assumptions -> u > 2 && m > 10]
Mathematica declares that the ...
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12
votes
2
answers
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Reduce not making full use of list of assumptions?
I have the following inequality, with conditions:
...
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12
votes
3
answers
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Assumptions allowing to calculate an elliptic integral
When I feed Mathematica the following integral:
Integrate[Sqrt[(A - x) (B - x)/x], {x, 0, B}]
it spits it back out without evaluating it. However, it can ...
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12
votes
2
answers
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Maximizing a function with assumptions
Using
f[s_] := Log[(s/r)^α ((α - 2) n0 r^α + 2 π Pmax ρ r^2)
/((α - 2) n0 s^α + 2 π Pmax ρ s^2)]/s
When I run the following line:
...
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12
votes
1
answer
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Assumption on the range of a function
I'm using value-defined function as set of parameter, i.e.
f[1] ===> first parameter
f[2] ===> second parameter
f[3] ===> third parameter
etc.
I would ...
- 909
12
votes
5
answers
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Limit of sequence of functions behaving strange
I'm trying to determine the limit of the sequence of functions
$$f_n(x)=\left(\frac{1}{\pi}\arctan(n x) + 1/2\right)^n.
$$
I define
...
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12
votes
0
answers
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Simplify and Sqrt, inconsistent behavior?
I have encountered some problems when using Simplify with expressions containing a square root and isolated a following test case
...
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11
votes
1
answer
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What exactly does GenerateConditions do?
Consider for example this strange behavior:
Integrate[1/x, {x, 0, Infinity}, GenerateConditions -> False]
(*0*)
I'd also like to know the difference between <...
- 1,217
11
votes
1
answer
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Is it possible to add some pattern to $Assumptions
I apologize if it is a too elementary question but I could not find the appropriate documentation so far.
My goal is simple. I would like to add some assumptions that are defined in terms of ...
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11
votes
1
answer
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Keeping Integrate from making unnecessary assumptions
I would like to evaluate the integral
$\int_{-\infty}^\infty \mathrm{d}x \, \exp\left(- a x^2 - x^4\right)$ for any real value of $a$. Mathematica 8.0.4 gives the following result:
...
- 213
10
votes
3
answers
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Reduce can't reduce an equation without appropriate assumptions
When there are three unknowns (x, y, z), Mathematica can solve it:
...
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votes
1
answer
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Linearity Assumption [duplicate]
I'd like to define a set of variables of this sort:
{K1[t],K2[t],...}
Adding a general assumption: all such variables are linear.
I'd like to do this to avoid ...
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votes
1
answer
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Is my expression too complicated for FullSimplify or am I doing something wrong?
I have a messily defined function $v(h, w)$ with $h, w \in \mathbb{R}$ and with a removable singularity at $h=1/2$, and I am trying to prove some of its properties using Mathematica. In particular I ...
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votes
4
answers
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How can I use assumptions with FindRoot?
I have something like
FindRoot[f[x], {x, a}]
Now I want FindRoot to constrain the solutions to 0 < x < 1. How can I ...
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4
answers
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Using Assuming with Reduce
I have the following code that includes Assuming to cut through irrelevant detail, or so I had hoped.
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5
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simplifying $\frac{\log x^a}{a} = \log x$
If one makes the assumptions $x>0,a>0$, then $\frac{1}{a}\log x^a = \log x$. Thus, in Mathematica, Simplify[1/a*Log[x^a], {a > 0, x > 0}] returns ...
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Mathematica gives wrong answer for an integral
Bug introduced in 9.0 or earlier, persisting through 13.2 or later
When I execute the following,
Integrate[ Exp[-w^2 + I w^3], {w, -∞, ∞}]
I get
...
PJR
9
votes
1
answer
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Is it possible to set a variable as a positive one in the whole notebook?
I'm having issues during integration due to the fact that Mathematica doesn't know if an undefined variable is positive or not (it gives me complexes which bothers me in the end).
For example I do ...
- 8,587
9
votes
3
answers
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Unknown function with arbitrary arguments assumption
Is it possible to define an assumption like this:
$Assumptions=f[__]>0
So that:
...
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9
votes
2
answers
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Problem with Identifying Complex Components
I am trying to isolate out the real and complex terms in a fairly large expression. During the process, I have made several assumptions that last throughout the entire process.
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votes
3
answers
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Simplify with Assumptions Sqrt[(expr)^2]
While trying to simplify expressions in the form Sqrt[(expr)^2] when expr>0 I noticed a peculiar behavior that was not ...
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1
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Adding irrelevant assumptions changes the result of Simplify
I've run into this problem a number of times. A typical example is
Simplify[Sign[k], {0 < A, 0 < B, A*Exp[2*y] < k, y > 1}]
which evaluates to $1$, ...
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Assumptions on unknown functions
I'm trying to do analytic calculations in a quantum mechanic harmonic oscillator basis. Specifically I want to be able to evaluate functions of the many particle density.
I define the following ...
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votes
0
answers
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When and why are Assuming and Assumptions not equivalent? [duplicate]
In this question there's an example of an integral where using Assuming and Assumptions give different results:
...
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8
votes
4
answers
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Simplify makes Mathematica forget that a matrix is Hermitian
Using Simplify with certain trivial assumptions makes Mathematica forget that a given matrix is Hermitian. See the minimal example below:
...
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votes
4
answers
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Attaching persistent assumptions to symbol definition
Is it possible to attach assumptions to a symbol? This relates to this question. Most of my work involves physical equations, i.e. there are basic assumptions on variables that will always hold true (...
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votes
1
answer
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Why Mathematica is treating the product of (specified) real variable as complex?
For the given matrix
...
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votes
2
answers
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How do I SetDelayed $Assumptions
For some reason,
$Assumptions := (Print["y"]; x > 0)
evaluates the RHS immediately.
I have code in which $Assumptions ...
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8
votes
1
answer
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evaluation of the sum of KroneckerDelta
I need help. I need to know why the next code doesn't simplify in Mathematica 10 but it does in Mathematica 8. I need some similar in version 10. What can I do?
...
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votes
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Why does Simplify work diferently for (a+b)/e versus (a+b+c)/e?
I am playing around with Simplify amd assumptions. I noticed that:
Simplify[x > (a + b)/e, x < (a + b)/e]
...
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8
votes
0
answers
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What is a "generic case"?
Introduction
With this question, I am coming back to a long-standing issue I have with Mathematica's concept of a "generically correct" result. The basic idea seems to be, vaguely, that if a ...
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votes
2
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Forcing Mathematica's Integrate to give more general answers
I have a simple gaussian integral: $\int^{\infty}_{-\infty}dx\:e^{i\alpha x^2}$.
If $\alpha \in \mathbb{R}$, then:
$$
\int^\infty_{-\infty} dx\; e^{i \, \alpha x^2} = \sqrt{\frac \pi {-i \alpha}} \...
- 607
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votes
1
answer
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How to best add assumption that many variables are positive?
I often need to check whether integrals are solvable in closed form and use a notebook with 5–10 variables that need to be assumed positive. Is there a better way of doing this than adding the clunky ...
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votes
2
answers
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Problem with Simplify, Sqrt, and Set: What's going on?
I am having some trouble getting Mathematica to simplify an expression of the form Sqrt[x]*Sqrt[1/x], where x>0. The problem ...
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votes
3
answers
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RSolve with assumptions
Bug noticed for Mathematica 8 and persisting through 11.3; Submitted to Wolfram, Inc. as CASE:3729158
I want to solve the following non-linear first order difference equation:
$$
k_{t+1} = (1-a) k_t^...
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