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# Questions tagged [algebra]

Abstract manipulation of symbols. Transforming an algebraic expression into the desired form.

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### Is AlgebraicRulesData magical?

I am trying to understand what AlgebraicRules is all about in the answer to this question. It apparently returns an ...
60 views

### Replacing value by another value

My question is that in Mathematica notebook when I write replacing commands, it didn't replace. In:= 2*x+y+1/.(x+y)->0 Out:=1+2x+y or ...
Im interested in counting the number of operations required to evaluate a given formula. Let me give you an example. Lets say I have entered the expression $\dfrac{\operatorname{Sqrt}[\operatorname{... 3answers 204 views ### How do I solve this equation with Mathematica? [closed] I've used Solve, Reduce, and NSolve, but I don't get anything $$\frac{w^{3w-20}-w^{w}}{w^{... 0answers 70 views ### Hafnian of a matrix Is there a Mathematica built-in function for the calculation of the Hafnian of a matrix? I am interested in the function as it appears naturally in the calculation of moments of a multivariate ... 1answer 116 views ### Parametric Curves to cartesian equation I have x=t^2-3 and y=t+2. I keep trying Eliminate and the output is always True. I just need to take these two curves and convert it to a Cartesian equation. ... 1answer 82 views ### Algebra deduction? I was trying to use Mathematica for some simple algebra deduction, but it didnt work. code: TrueQ@(Sqrt[(e0 u0)/(e1 u1)] == Sqrt[e0 u0]/Sqrt[e1 u1]) Any ideas ... 0answers 47 views ### Grassman and Clifford algebras as quotients of the tensor algebra I've been working with tensors in Mathematica; it's great to have something like TensorProduct built-in with linearity and everything. Maybe you can take advantage of these structures to work with ... 1answer 39 views ### Assuming x real, simplifying or refining Im[1/(x+i)] doesn't yield anything I think it is straightforward from the title, Simplify[Im[1/(x+I)], x > 0] spits out, Im[1/(x+I)] while I would have ... 0answers 20 views ### Expressing Numbers with Rational Denominators (Surd Form) [duplicate] Is there a command which expresses given real numbers in surd form (when possible)? That is, a form where any rooted terms are placed in the numerator, and the denominator is rational. Here are some ... 0answers 41 views ### Algebraic manipulation on removing common factor outside d[i,j] and M[i,j] are elements of size arrays of size 2x2 After some manipulations I get this as Output ... 1answer 48 views ### Abelianness-forcing number Q In the theory of finite abstract group, abelianness-forcing number n is characterized as a positive integer with standard factorization n=p_1^{k_1}p_2^{k_2}\cdots p_r^{k_r} with k_i \le 2 and ... 2answers 45 views ### Replace rules change dimension This is absolutely driving me crazy, I don't know if this is a bug or what, but replace rule sometimes change dimension of my data. Say I have data: ... 0answers 33 views ### Ordering of Eigenvectors [duplicate] I am interested in computing the derivatives of the eigenvalues of a certain n\times n Hermitian matrix M(t). I know I can do this easily since I know the exact expression for \dot{M}, and the ... 2answers 66 views ### Apparent contradiction in double summation I have two expressions which, if my maths is correct, should both be true. But Mathematica doesn't agree. I can take the expression E^(-n^3) out of the single ... 1answer 60 views ### Sum of powers of zero [duplicate] I would like to calculate the following sum Sum[0^(k-a), {k, 0, Nin}] for a positive integer a. With considering 0^0=1, my expected answer of the sum is 1, ... 4answers 197 views ### Simplifying simple signed expression ( such as -x(x-1) \to x(1-x) ) based on assumptions Context I would like to simplify expression involving, say, (x-1) or (x^2-1) when I know that |x|<1 so that the global ... 1answer 30 views ### How to change the form of the answer? [duplicate] Reduce[x^2 + y^3 == z && x + 2 y == 3 z + 1 && x y z != 0, {x, y, z}] you get ... 2answers 46 views ### How to manipulate sequences of inequalities? I am trying to write some symbolic inequality proofs in Mathematica. What would be a clean way to make the inference that a >= b and ... 3answers 813 views ### How can I implement anti-commuting (Grassmann) numbers (variables)? I am looking for a way to define anti-commuting numbers (variables) in Mathematica. Let say we have a set of four variables like {x_1,x_2,x_3,x_4} from which I need to get all possible permutations, ... 1answer 25 views ### Trying to apply Jensen's inequality to a complicated symbolic expression I have a somewhat complicated inequality expression like this: ... 1answer 178 views ### Symbolic non-commutative algebra Consider 3 non-commutative elements A,B,C and we have the relation CB=\alpha BC. I want to compute things like : (A\otimes BC ) ( B \otimes B) = AB \otimes \alpha B^2C Is there any package ... 2answers 136 views ### How can I define operators that implement the algebra of sets? I need to define some operators with properties like idempotence and distribution over union and intersection so that Mathematica can symbolically simplify expressions. How do I define such operators? ... 2answers 65 views ### How to get Mathematica to simplify/refine a Polygamma expression of fractions I got the following ugly ev[n] as the least complicated answer to a Fourier coefficient integral Integrate[Cos[t]*Sin [(2 n + 1)*t]/Sin[t], {t, 0, Pi/2} ... 1answer 142 views ### How to implement split-complex numbers? For those who do not know, the split-complex numbers are an analogue to the complex numbers where J is defined such that J^2=1 but J\ne\pm1, so they are all of the form a+bJ. By using ... 1answer 217 views ### Factorization of a fractional multivariate polynomial Suppose I have given a fractional multivariate polynomial ... 0answers 39 views ### Find a matrix that are unitarily equal to the given matrix I have four 5\times 5 matrices, P_i, Q_i (i=1, 2) as follows: P_1=\begin{pmatrix} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & -... 3answers 96 views ### Finding the integer terms of a binomial expansion [closed] What functions can I use to find how many integer terms the following expression has?$$\left (\sqrt{19}+\sqrt{95}\right )^{1995}$$Edit 1 In the development of that binomial, at some point ... 0answers 45 views ### Function ellipticAdd to add points belonging to an elliptic curve y^2 = x^3 + a\,x^2 + b\,x [duplicate] In the EllipticLog WRI web page, there is a function called"ellipticMultiply defined as: ... 1answer 88 views ### Symmetrize a polynomial forgetting the commutativity property of multiplication I need a script to authomatically symmetrize a given polynomial. For example, if the input is xy the output should be ... 2answers 248 views ### Solving an equation with vector coefficients I want to solve (ct)^2 = d(t)\cdot d(t) for t, where d(t) = \frac{1}{2}at^2 + vt + r Where a, v, and r are all 3-dimensional vectors in Cartesian coordinates. How can I do this? 0answers 63 views ### Connectivity of semi-algebraic set I am given the following semi-algebraic set:$$ \{ x= \begin{bmatrix} x_1,x_2,x_3,x_4,x_5 \end{bmatrix} ^T\in\mathbb{R}^5| -2 \leq (1 - x_2x_3)x_5 - 2x_4x_3x_1 \leq 1.5,\\ ~ -1 \leq x_1 \leq 30,... 0answers 65 views ### Some Mathematica textbooks specialized for use in (nontrivial) algebra? So, Mathematica was constructed as a computer algebra system, but most textbooks focus on programming, mathematical problems of secondary school type or numerically-technical specialization (matrix, ... 1answer 90 views ### Conditions on parameters in Reduce i have a system of equations in which there are two parameters F, G. I choose F,G positive. the code is: ... 2answers 818 views ### Solving equations with subscripted variables A student of mine tried: Solve[1/R == 1/Subscript[R, 1] + 1/Subscript[R, 2], R] which did not work. We then tried: ... 0answers 83 views ### How do I separate 2 variables to be independent from each other in the equation? I have an equation namely ... 1answer 42 views ### Removing denominator and rearranging by powers of$t$Suppose the following function$f(t)$$$f(t)=x^2+y^2+2m(u-y)-u^2,$$ where $$m=\frac{(t-2)(1-t^{2}+\sqrt{1-t^{2}})}{t(1+\sqrt{1-t^{2}})(1-t-\sqrt{1-t^{2}})},$$ and $$u=\frac{t}{1+\sqrt{1-t^{2}}}.$$... 1answer 48 views ### I am a beginner and How to read the Result of Reduce [duplicate] I am a beginner and cannot read the result given by the reduce command kindly help. I used: ... 1answer 107 views ### How to stop GroebnerBasis from automatically normalizing? I need to compute the Groebner basis modulus a set of prime without normalizing the Groebner basis output. Is this possible? Example: ... 2answers 702 views ### Removing higher order terms I have a very long expression in terms of the three functions u1, u2, u3. I am writing below only a small number of terms. I would like to define a rule that keeps terms of order three or less of any ... 0answers 47 views ### Defining an abstract multiplication over finite indices I would like to define a map (a "multiplication" denoted$\otimes$) over the finite set of symbols$G=\{a,b,c,d,e,f,g,h\}\$. I would like to define several rules like $$a \otimes b= \{b \}$$ $$a \... 4answers 200 views ### How to separate integers and radicals from a term? If I have a variable such as r = 1 + Sqrt + Sqrt how can I separate that into two separate variables with the rational and irrational parts? i.e. ... 1answer 192 views ### Efficient implementation of the divided difference Question. I am looking for more efficients ways to compute Newton's divided difference, i.e. the operator$$\partial : f(x,y) \mapsto \frac{f(x,y)-f(y,x)}{x-y} \ , $$for the case where f is a ... 1answer 92 views ### Summation returns unevaluated Please help me do this summation as Mathematica returns the same expression: ... 6answers 277 views ### Making strict replacements in Mathematica My question is quite a simple one, but I have not been able to find a solution yet. Say I have terms of the form e.g 1/n1/n2/n3/n4 and ... 1answer 96 views ### Factoring expression with rational powers To any great Mathematica-matician. Why Mathematica can’t factor this Factor[-1+x^(2/3)] I know that Factor mainly targets ... 0answers 30 views ### Computational discrepancy for plugging in equivalent forms into an expression When the following 9th root of unity is raised to the 6th power a 3rd root of unity is returned. (Power[-(1/2) + (I Sqrt)/2, (3)^-1])^6 // N -0.5 - 0.866025 I ... 1answer 60 views ### Relabeling/matching variables of big data (in MultiplicationTable) Let A and B be two sets of tables (from multiplication tables of a group, 24 by 24 as rows by columns), how can we effectively (and possibly also efficiently) find a way to map between them, if two ... 1answer 70 views ### Relabeling and matching variables (in MultiplicationTable) Suppose we have a set of data given here as the multiplication table of 8 elements labeled {1,2,3,4,9,10,11,12}:$$ \begin{array}{cccccccc} 1 & 2 & 3 & 4 & 9 & 10 & 11 & ...
I try to use <<Combinatorica or call IntervalSlider; Needs["Combinatorica"] or call ...