Someone who has patience enough might want to add the plots. I gave it two options: Options = ] &] ĪspectRatio -> 1, Frame -> True, Axes -> True] (I'm not sure, but maybe I posted it on the MathGroup. Here's a procedure I've been using since version 5, it might provide similar features in versions prior to the introduction of Value. FullSimplify).Ah, they finally implemented it in version 10, then! Solve is the Mathematica function used for symbolically solving a polynomial equation or set of equations. To solve systems or sets of equations in Mathematica, one has to use functions such as Solve, NSolve, and Reduce. Reduce[ x^2 + y^2 83/84, y -> 31/18}, *)ģ) Solve tends to be less thorough than Reduce in order to return an answer faster (somewhat like Simplify vs. Solve::fdimc: When parameter values satisfy the condition r ∈ Reals, the solution setĬontains a full-dimensional component use Reduce for complete solution information. We have the same issue with Reduce.Įxample : Solve cannot find solutions in the real domainĬonsider a simple symbolic case in the real domain where Solve does not work even with Ma圎xtraConditions -> All : Solve I am solving the above set of three equations using Solve in Wolfram Mathematica but I get the error message as Solve::nsmet: This system cannot be solved with the methods available to Solve. Inequalities are real, while all other quantities are complex. Solve assumes by default that quantities appearing algebraically in NDSolve can also solve some differential-algebraic equations, which are typically a mix of differential and algebraic equations. It can handle a wide range of ordinary differential equations as well as some partial differential equations. Using Ma圎xtraConditions -> All in Solve provides complete solutions for algebraic equations, nevertheless we have to emphasize that sometimes we might better work with Reduce rather than Solve (regardless of any options added) because replacement rules may appear not a good fit in description of solutions in the real or complex domain to algebraic equations as well as to trancendental equations˛ Distinction between genericity and completness does not make sense in the Integers, an example provided below. The Mathematica function NDSolve is a general numerical differential equation solver. Solveexpr, vars, dom solves over the domain dom. (The Mathe- maticafunction NDSolve, on the other hand, is a general numerical differential equation solver. Solve returns lists of replacement rules yielding generic solutions.Īn important step toward more complete description of solution sets was a new option of Solve in Mathematica 8, namely Ma圎xtraConditions (default value 0). Solveexpr, vars attempts to solve the system expr of equations or inequalities for the variables vars.Reduce returns results of computation as boolean formulae and gives complete description of solution sets.There is much more than a little difference between them. Reduce and related functions use about 350 pages of Mathematica code The code for Solve and related functions is about 500 pages long. Its a good idea to begin user symbols with lower case, so they dont override Mathematica definitions. You can use the Rule by a Replace, for which the shortcut is /. In Some Notes on Internal Implementation especially in Algebra and Calculus one finds interesting subtleties and differences between these two functions, e.g. Solve is giving you a Rule for T, which is much more polite than setting the variable T to some value.
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