stream Otherwise, it is hard to interpret what the data means. Connect with users of Wolfram technologies to learn, solve problems and share ideas, Community posts can be styled and formatted using the. Thebundleofpackagescanbedownloadedfrom https://github.com/EverettYou/Mathematica-for-physics Toinstalleverything: 1.unzipthisrepositoryinafolder, 2.openinstall.minMathematica, 3.clicktheRunPackagebuttontothetopright, 4.quitMathematicaandrestart. Is it safe to publish research papers in cooperation with Russian academics? While the mark is used herein with the limited permission of Wolfram Research, Stack Exchange and this site disclaim all affiliation therewith. /S /Transparency Wolfram Natural Language Understanding System. ?#KdJ'qvyovEMLEKXG!B/|! Ue1mgnEp{bApvhm{C\hoN/.dM#Z:R{(e_xb8}yPA8A%|>Dvy"e!2|gg:.gL=@ u6[LQeAxtgF(DT. To solve the Lagrange-multiplier system above, use the following command, which invokes the built-in Solve command. Wolfram Language & System Documentation Center BUILT-IN SYMBOL TableForm TableForm [ list] prints with the elements of list arranged in an array of rectangular cells. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Volume 31, Number 1, Summer 2011. Using Mathematica on Lagrange-multiplier ProblemsCopyright 1997, 1998, 2000 by James F. Hurley, Department of Mathematics, University of Connecticut, Storrs, CT 06269-3009. The key point is that for any value k, the function f assumes the value k precisely on the level curve f(x, y) = k. To find the maximum or minimum value of f on the curve g(x, y) = 0, it is thus enough to plot the level curves of f and find the largest and smallest values of k for which the curve g(x, y) = 0 intersects some level curve f(x, y) = k. The following figure illustrates the idea for the problem from Example 10.4 of Section 4.10: find the maximum value of f over the curve 2 x 4 + 3 y 4 = 32, if the formula for f is f(x, y) = ( x 2 + y 2 ) 1 / 2 . Finding distribution parameters of a gaussian mixture distribution Reading in scientific notation from C++ to Mathematica How to draw Fractal images of iteration functions on the Riemann sphere? Technology-enabling science of the computational universe. It probably just needs some Map or MapAt command, maybe combined with a Transpose in order to apply to rows instead of columns - but I can't figure out the correct syntax for addressing an entire column (or row).. Wolfram Community forum discussion about How to Export a Table as an Image?. This notebook illustrates how to handle the problem. Conjecture: a(n)/n -> sqrt(2)., and -1 < sqrt(2)-a(n)/n < = -1+sqrt(2) for n >= 1. In this case, it's clear which value of f is the maximum and which is the minimum, since Mathematica calculates only two function values, of which one is positive and the other negative. Mathematica is available on Windows, macOS, Linux & cloud, Questions? The result is that the column heading has become a table heading for the inner table. MatrixForm, Enable JavaScript to interact with content and submit forms on Wolfram websites. The function CycleGraph, which you are using, is a built-in function and is not understood by the Combinatorica package. %PDF-1.5 Have fun! /Height 557 ArrayFlatten /Width 561 Semicolons at the end of lines suppress printing results of computations. For the given f and g, the following short routine carries that out. Wolfram Research. of Physics/Mathematics. where the first line is the x axis, but the y column is the first number of the following lines 565), Improving the copy in the close modal and post notices - 2023 edition, New blog post from our CEO Prashanth: Community is the future of AI, ImagePadding or other means of getting whitespace when the PlotLabel is a Column or Grid, An issue with formulas typesetting in Grid & Column, Incrementally revealing Grid (or TableForm) entries. I usually do something like: ExportString[myTable, "TSV"]//CopyToClipboard with the table in the variable myTable. (1988). how to apply AccountingForm to TableView without affecting the row/column labels? To subscribe to this RSS feed, copy and paste this URL into your RSS reader. show complete Wolfram Language input Related Examples If you want the frame, too, this might work: Great for images. Curated computable knowledge powering Wolfram|Alpha. rev2023.4.21.43403. Try the following command to obtain decimal expressions for the numbers the last routine gives: { { - 3.5777087639996634` , 1.7888543819998317` , - 8.94427190999916` } , { 3.5777087639996634` , - 1.7888543819998317` , 8.94427190999916` } }, Converted by Mathematica (June 11, 2003). /XObject << /x6 6 0 R >> Revolutionary knowledge-based programming language. << View. Central infrastructure for Wolfram's cloud products & services. I looked up the possible options for TableForm, but I could not find a relevant one. Has the cause of a rocket failure ever been mis-identified, such that another launch failed due to the same problem? Mathematica Stack Exchange is a question and answer site for users of Wolfram Mathematica. Technology-enabling science of the computational universe. Show vector, matrix and general arrays in tabular form: Define both horizontal and vertical alignments: Only use tabular formatting for the outermost dimension: By default the outermost dimension is a column: Format the first dimension as a row instead: Explicitly specify the spacing between rows and between columns: Multiplication table for the cyclic group : TableForm formats arrays in a tabular form: MatrixForm formats arrays using standard matrix formatting: Grid formats two-dimensional arrays as a grid: Use MatrixPlot to visualize the structure of large arrays: Use ArrayPlot to visualize the structure of large discrete arrays: Use Style to affect the display of TableForm: Use any number form such as ScientificForm or BaseForm to affect the display of numbers: The typeset form of TableForm[expr] is interpreted the same as expr when used in input: Copy the output and paste it into an input cell. . How should I write a function to be used in Apply in Mathematica? F[x_, y_] := 2 x - yG[x_, y_] := x^2 + y^2 - 16gradf = {D[F[x, y], x], D[F[x, y], y]};gradg = {D[G[x, y], x], D[G[x, y], y]};Print["grad f = ", gradf]Print["grad g = ", gradg], grad f = { 2 , - 1 } SequenceForm grad f = 2 -1, grad g = { 2 x , 2 y } SequenceForm grad g = 2 x 2 y. I tested it and it works perfectly. Apply EuclideanDistance at a certain level in Mathematica, How to insert a column into a matrix, the correct Mathematica way, Multiple statements in mathematica function. Elegant, readable, and works with in-line code, e.g., when manipulating a list before plotting it, like multiplying the x-column by two: ListPlot[Map[MapAt[Function[x, 2 x], #, 1] &, list]], Mathematica: How to apply function to a certain column of a table. To complete the solution to the example, just compute the value of f at the candidates Mathematica found. It is not clear whether you want to modify the existing table, or to create a new table with modifications, leaving the original intact). With Inactive, it is easier than ever to create tables of values. Connect with users of Wolfram technologies to learn, solve problems and share ideas, Hi, I have a set of data in the table format Can you suggest a neat way to achieve it? So it's a simple matter to modify only that column: will apply f to each element of the nth column of mat. /Filter /FlateDecode Does the 500-table limit still apply to the latest version of Cassandra? A multiplication table for the numbers 1 through 7. SpanFromAbove Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. /I true If you work on a project, save it frequently and make backups. << Mathematica: How to apply function to a certain column of a table. stream The preeminent environment for any technical workflows. /Resources 2 0 R Bill White Bill White. It also contains the assignement at the very end. What does "up to" mean in "is first up to launch"? https://reference.wolfram.com/language/ref/TableForm.html. So, for instance, will apply Sin[Cos[#]]& to each element of the second column, while, will multiply each element on the second column by s, One versatile approach is to use ReplacePart. xX[o6~I2I$O4 -X`AgHSQ{.m,AwT)%Jctts4L\Bet>=UM}s:mFqV]s yi\Z?fJ-*K"DirAS} W2eEoqZ$"h#0T9>\)T3%,0dtHJ4 J?T}s]a8d3C>f.NSRBeJQRzZ*`.a`$nMZ?4qc7G]rwprD'.u;ZVkMW]3;*kMtHpE The best answers are voted up and rise to the top, Not the answer you're looking for? Sorry I missed that. Improve this answer. To find all candidates for extreme values of f subject to a constraint g(x, y) = 0, solve the system of equations (3)f(x, y) = g(x, y),g(x, y)= 0for x, y, and . 4. Has the Melford Hall manuscript poem "Whoso terms love a fire" been attributed to any poetDonne, Roe, or other? So x={1,2,3,4}, y={10,20,30} and f(x,y) are the remaining data. Chain Rule 5.3 then makes it easy to differentiate g(x, y) = 0 with respect to x: (1)0 = d dx [g(x, y)] =g(x, y) ( x x , y x ) = g(x, y) (1, y'(x)). Try it! In [1]:= Out [1]//TableForm= A multiplication table for the numbers 1 through 7. 9 0 obj To find the points of intersection of the constraint curve 2 x 4 + 3 y 4 = 32 and the level curves of the function f, it might be feasible to solve g(x, y) = 0 for y as a function of x. What should I follow, if two altimeters show different altitudes? I attached a couple of documents to clarify what's going on here. This notebook will be your guide to get started. >> /Type /XObject 4. Content in a mathematica file is organized as cells. To create a new file and put an expression (mathematica output) in the file wiping out previous entriesin the file: expr >>myfile (same as Put[data, "myfile"])To append an expression to an existing file: expr >>>myfile (same as PutAppend[data, "myfile"]) 8 0 obj If so, you could substitute that expression into the level curve equation f(x, y) = k, where k corresponds to the level curve tangent to the constraint curve at each point of intersection. I too am now struggling to plot output from a function of two variables. The Mathematicadifferentiation command has the formD[F[x, y,. What were the most popular text editors for MS-DOS in the 1980s? Wolfram Research (1988), TableForm, Wolfram Language function, https://reference.wolfram.com/language/ref/TableForm.html. Browse other questions tagged, Where developers & technologists share private knowledge with coworkers, Reach developers & technologists worldwide, Another elegant way to do it is like the cumulative functions in C: table[[All, 2]] *= 10. Central infrastructure for Wolfram's cloud products & services. Revolutionary knowledge-based programming language. The following TableForm command is a convenient means to do so. FindCycle not working as expected for multigraph How to add lines in TableForm How to get short definition of all built in Mathematica Functions? The preeminent environment for any technical workflows. LINKS: Clark Kimberling, Table of n, a(n) for n = 1..10000 /CS /DeviceRGB stream In row n, for n>1, the first two terms are 1 and n-1, and the last two are F(n) and F(n), where F = A000045 (Fibonacci numbers). It then follows immediately from (1) that the gradient is perpendicular to the nonzero vector (1, y'(x)). In addition to original research and reviews of new books, Russell publishes new texts and textual studies, discussions, bibliographies, indexes, and archival lists. If total energies differ across different software, how do I decide which software to use? TableFormWolfram Language Documentation - DatasetWolfram Language Documentation TableForm[list] prints with the elements of list arranged in an array of rectangular cells. Make the headings bold and extend the second heading into the third and fourth columns with SpanFromLeft: Add a column of row headings to the grid. /Filter /FlateDecode Technology-enabling science of the computational universe. >> If you work on a project, save it frequently and make backups. Wolfram Natural Language Understanding System. pXc$/JEYt4MAYX,TnW{df)ep)H/f Noticethat f(0) =sin 0 j0j is unde ned so we stop at 0:01 . Question arose as I tried to automate a result. /ColorSpace /DeviceGray 2 0 obj Details and Options Examples open all Basic Examples (1) Show vector, matrix and general arrays in tabular form: In [1]:= In [2]:= Out [2]= In [3]:= Out [3]= In [4]:= In [5]:= TableForm 222.) >> xeMN0>,A"ob/THB@I ne{(naBh' How can I plot these data in a 3D like form? Was Aristarchus the first to propose heliocentrism? MapAt function accepts the following Part specification: Another compact solution I found is using Map and MapAt: Now apply the function f to the second column: Thanks for contributing an answer to Stack Overflow! So Marco's first line of code exactly answers your question? Start with some data Here is data on objects and their dimensions: In [9]:= Format the data as a grid Make a grid of the data: Out [10]= Specify how the data in the grid should align Use the TableAlignments option to specify how items in columns should align: Out [11]= In your second graph you see that the data coordinates are 1 to 5 for x and 1 to 5 for y. /Interpolate true This holds in particular at any point P at which f has an extreme value on the constraint curve g(x, y) = 0. Have fun! Thanks! The This will generate a table without a title. The coordinates of vectors are in braces, with commas between them. There is a hack that has some added advantages - in particular as a by-product you also get a vector graphics version of your plot that can be resized while keeping all relative sizes at the correct proportions:. Can you suggest a neat way to achieve it? candidates = Solve[{gradf == lambda gradg, G[x, y] == 0}, {x, y, lambda}], { { lambda "\[Rule]" - 5 8 , x "\[Rule]" - 8 5 , y "\[Rule]" 4 5 } , { lambda "\[Rule]" 5 8 , x "\[Rule]" 8 5 , y "\[Rule]" - 4 5 } }. Use MathJax to format equations. Making statements based on opinion; back them up with references or personal experience. Thanks for contributing an answer to Mathematica Stack Exchange! Effect of a "bad grade" in grad school applications. MathJax reference. (There are two preliminary partial figures first, which then combine to give the final figure. Instant deployment across cloud, desktop, mobile, and more. p*3,++"" Sa1("\*S1kE%joT[sYFR*h|j2NT>UDSNT>UFReL.U*xEsHT.U7HoL #g0r'J Looking for job perks? Browse other questions tagged. . . Learn more about Stack Overflow the company, and our products. 1988. Let's say I want to make a title "Bravo" on top of the table (which is center-aligned). TableForm should be used for viewing data in an easy to read format, but shouldn't be used as a wrapper when storing data. The preeminent environment for any technical workflows. Let's say I want to make a title "Bravo" on top of the table(which is center-aligned). Note: Only the first five people you tag will receive an email notification; the other tagged names will appear as links to their profiles. evaluate f at every candidate (x, y) that solves the system (3) the largest value that results is the maximum of f subject to g(x, y)= 0 the smallest resulting value is the minimum of f subject to the constraint. I recognize this was 8 whole years ago, but did you ever get a sufficient answer? BTW: If one is just after a multiplication of, say, column 2 of 3 total, a matrix multiplication A.DiagonalMatrix[{1,s,1}] will also do the trick. (2)f(x, y) = g(x, y) for some real number !=0.If f is 0, then (2) still holds: = 0 makes it true.This leads to the Lagrange multiplier algorithm.Lagrange Multiplier Algorithm 10.2. Why in the Sierpiski Triangle is this set being used as the example for the OSC and not a more "natural"? Instant deployment across cloud, desktop, mobile, and more. Connect and share knowledge within a single location that is structured and easy to search. Thank you for your speedy reply Rohit. How to combine several legends in one frame? /Contents 3 0 R @`x,XZ;/*0>80{?MV~IjU?Z How a top-ranked engineering school reimagined CS curriculum (Ep. endobj What were the most popular text editors for MS-DOS in the 1980s? Notes:1. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Redo the last table starting fromx= 0:01 and ending atx= 0:001 in steps of 0:001 : fx, 0.01, 0.001,-0.001g. Central infrastructure for Wolfram's cloud products & services. Contact a Wolfram expert. Note: Only the first five people you tag will receive an email notification; the other tagged names will appear as links to their profiles. surprisingly simple.. use TableForm or Matrix Menu NEWBEDEV Python Javascript Linux Cheat sheet Find centralized, trusted content and collaborate around the technologies you use most. ]}, Enable JavaScript to interact with content and submit forms on Wolfram websites. Knowledge-based broadly deployed natural language. /BitsPerComponent 1 (f)The following uses this formulation to show 5, 10 and 15 bars with the properties stated in (b) covering the interval [ 1; 2]. So consider the problem of finding the maximum and minimum values of a function f on a curve with equation g(x, y) = 0. Wolfram Language. This notebook will be your guide to get started. Find the maximum and minimum of fon the circle x 2 + y 2 = 16, if f(x, y) = 2x - y.Solution. I have export of a PNG file working fine for a plot. (Compare Figure 10.3 of the text, p. 3. Actually I just want to multiply all elements in that column with a scalar, but the application of a general function would be fine as well. Issue. 2. Instant deployment across cloud, desktop, mobile, and more. Print["x", "", "y", "", " f(x, y)"]Print["========", "", "========", "", "=========="]{x, y, F[x, y]}/.candidates//TableForm, x y f(x, y) SequenceForm x y f(x, y), ======== ======== ========== SequenceForm ======== ======== ==========. I was missing the nested map ( /@ ) inside the MapAt in my own attempts. What are the advantages of running a power tool on 240 V vs 120 V? %PDF-1.3 Which was the first Sci-Fi story to predict obnoxious "robo calls"? << /Length 10 0 R TextString can not convert general TableForm, Equalizing the column widths in the rows below the title row of a grid, Extracting arguments from a list of function calls, The hyperbolic space is a conformally compact Einstein manifold, Tikz: Numbering vertices of regular a-sided Polygon, tar command with and without --absolute-names option. Curated computable knowledge powering Wolfram|Alpha. Instant deployment across cloud, desktop, mobile, and more. Example. To produce the figure, hit the Enter key (at the lower right of the keyboard) after the last command of the following Mathematica routine. Ak@>IDVZ(^daL]+mzX\}ag!2%5yZ)LfJf\ep!{R"J76LmW>;-eM@rYL{I8G58"x!T|\AA1>h4 Since g(x, y) = 0 defines y as a differentiable function of x, calculation of that derivative proceeds just as above: d dx [f(x, y(x))] =f(x, y) ( x x , y x ) = f(x, y) (1, y'(x)). How a top-ranked engineering school reimagined CS curriculum (Ep. "v-a92j}mX%H=W6C5;ennN. << /Length 4 0 R Dataset gives a quick, left-aligned view of tabular data in an array: When the data is a list of associations, Dataset displays the association keys as column headings: For detailed control of formatting, use Grid. TableForm is a simple alternative to Grid. Making statements based on opinion; back them up with references or personal experience. When defining functions in Mathematica, the right subscripted underscore character must appear with the initial occurrence of each variable to the left of the := sign. Row Curated computable knowledge powering Wolfram|Alpha. The obstacle to doing so by hand is the difficulty (or even impossibility) of solving (3). Learn how, Wolfram Natural Language Understanding System, whether to arrange dimensions as rows or columns, how many spaces to put between entries in each dimension. /Filter /FlateDecode All rights reserved, The method of Lagrange multipliers is useful for finding the extreme values of a real-valued function f of several real variables on a subset of n-dimensional real Euclidean space determined by an equation g(x) = 0. rev2023.4.21.43403. << /Type /Page endobj Revolutionary knowledge-based programming language. >> /OJ$+3 x5 1Hy.a{zua(=ePX0V6; N zca!{k`Y2~23~e_Cfh@>T}T[ux] m}D1=f 8q 6e}0a8pbN3aHxf'wsi`i?P 10#XxU1v2{X6$g:2Y|%@fzu4#K|g^9%v]00ex@1bE 354 is interpreted as {{1,2},{3,4}}: When an input evaluates to TableForm[expr], TableForm does not appear in the output: Out is assigned the value {{1,2},{3,4}}, not TableForm[{{1,2},{3,4}}]: Even when an output omits TableForm from the top level, it is not stripped from subexpressions: The output does not have TableForm in it: However, the variable e does have TableForm in it, which may affect subsequent evaluations: The determinant is not evaluated due to the intervening TableForm: Assign variables first and then apply TableForm to the result to maintain computability: MatrixForm Grid TextGrid GraphicsGrid TableView ArrayPlot PaddedForm. The Combinatorica package is now considered obsolete and not compatible with Mathematica's built-in Graph theory functionality. Technology-enabling science of the computational universe. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. {{1,2,3,4},{10,2,5,6,5},{20,1,3,4,7},{30,3,1,6,9}} Part of the issue with the data is that it should form a complete square or rectangle of numbers. Wolfram Language & System Documentation Center. Here is data on objects and their dimensions: Use the Alignment option to specify how items in columns should align: Add a row of column headings to the grid. It's actually a CSV (e.g. For this derivative to be 0, note that the gradient of f is either 0 or else must also be perpendicular to the vector (1, y'(x)). Is there a generic term for these trajectories? MIP Model with relaxed integer constraints takes longer to solve than normal model, why? Subject Wolfram Technology > Front End > Saving and Exporting Downloads TableExport.nb (11 KB) - Mathematica Notebook Software engine implementing the Wolfram Language. Revolutionary knowledge-based programming language. Column Revolutionary knowledge-based programming language. To illustrate, compare what follows to hand solution of the following example from the next edition of the text. What differentiates living as mere roommates from living in a marriage-like relationship? )USchA MX TableForm[{{1, 2, 3, 4}, {10, 2, 5, 6, 5}, {20, 1, 3, 4, 7}, {30, 3, 1, 6, 9}}] %PDF-1.5 Curated computable knowledge powering Wolfram|Alpha. formatting grid-layouts Share Improve this question Follow 34 This is the third of an apparently endless series of talks on how to use Mathematica in general relativity. Why typically people don't use biases in attention mechanism? This is a place where Mathematica's built-in Solve command can sometimes help. Central infrastructure for Wolfram's cloud products & services. Yes! ]}, @online{reference.wolfram_2022_tableform, organization={Wolfram Research}, title={TableForm}, year={1988}, url={https://reference.wolfram.com/language/ref/TableForm.html}, note=[Accessed: 01-May-2023 Say to the i-th column of a (m x n) table. ],z], where the last variable specifies the one with respect to which to carry out the differentiation. Table[{x, NumberForm[N[f[x]],9]}, {x, 0.1, 0.01, -0.01}]//TableFormThis table givesxandits corresponding value of f(x) starting fromx= 0:1 and ending at x= 0:01 in steps of 0:01 . In the definition below, I've added 0 to the first element of the data: The preeminent environment for any technical workflows. To learn more, see our tips on writing great answers. o/ LZ6[?qF 0d$ {nYJ-2q,CipK[!t#aNYC5|L.;_8R12tV Grid[{TableForm[paretoPickF2[newlist, #, .5, Less]] & /@ {2, 3, 4}}, Dividers -> All] Tags: Filtering List Manipulation Performance Tuning. >> You really don't need to know the value of , so if possible you can eliminate and solve for all pairs (x, y) that satisfy (3). Cells can be evaluated by grabing the bracket to the right, holding . SE?IgH.ac1 ht8YH "2p>a94;=& 9c&17&}I'! Wolfram Language & System Documentation Center. Parabolic, suborbital and ballistic trajectories all follow elliptic paths. Software engine implementing the Wolfram Language. From: Mathematica by Example (Sixth Edition), 2022 View all Topics Add to Mendeley About this page CONSEQUENCES OF {D [0,1], V {0,1}}} THEORY /Font << /Parent 1 0 R Which ability is most related to insanity: Wisdom, Charisma, Constitution, or Intelligence? 4 0 obj Content in a mathematica file is organized as cells. For me I wanted x={1,2,3,4} and y={10,20,30}. Out[4]= {20, 50, 80} In[5]:= table//TableForm Out[5]//TableForm= 1 20 3 4 50 6 7 80 9 Share. Yeah, that works. In [2]:= Out [2]//TableForm= Create a nicely formatted table. Knowledge-based, broadly deployed natural language. WolframAlpha.com WolframCloud.com All Sites & Community Resources. Learn how, Wolfram Natural Language Understanding System, Fast Introduction for Programmers: Associations. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Mathematica can compute the gradients of f and g by symbolic differentiation. Use the TableAlignments option to specify how items in columns should align: Add a row of column headings to the grid: You can add column and row headings to the contents of a Grid programmatically using ArrayFlatten: Grid % endstream Looking for job perks? Wolfram Natural Language Understanding System. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Thus, if f is nonzero, then it is parallel to g, that is. Buy Comments? TableForm [list] This will generate a table without a title. Generating points along line with specifying the origin of point generation in QGIS. For example, consider a list with depth two and a title. Instant deployment across cloud, desktop, mobile, and more. 565), Improving the copy in the close modal and post notices - 2023 edition, New blog post from our CEO Prashanth: Community is the future of AI. For example, to apply f to column 3 of mat: The following multiplies each entry by 10: However, a 'quick' way to do this it as follows: (Unlike the first method, all entries in column 3 of mat are now modified. Products& Services Wolfram|One Mathematica Wolfram|Alpha Notebook Edition Finance Platform System Modeler TableForm. How about saving the world? ), Needs["Graphics`ImplicitPlot`"];ContourPlot[(x^2 + y^2)^(-1/2), {x, -3, 3}, {y, -3, 3}, ContourShading -> False,PlotPoints -> 60, ContourSmoothing -> Automatic];Plot[{(32/3 - 2 x^4/3)^(1/4), -(32/3 - 2 x^4/3)^(1/4)}, {x, -2, 2}, PlotStyle -> RGBColor[0, 0, 1]];Show[%, %%, AspectRatio -> Automatic, AxesLabel -> {x, y}]. Connect and share knowledge within a single location that is structured and easy to search. "TableForm." My question is rather simple. /MediaBox [ 0 0 612 792 ] Software engine implementing the Wolfram Language. You must use the double equal sign when specifying an equation for Mathematica to work on.
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