Sage provides extensive 2D plotting functionality. The underlying rendering is done using the matplotlib Python library. Notice that the aspect ratio of the above plot makes the plot very tall because the plot adopts the default aspect ratio of the circle to make the circle appear like a circle. If you want the vertical units to be twice as big as the horizontal units, specify an aspect ratio of The figsize option adjusts the figure size.

The default figsize is 4.

SageMath Plotting and Graphics

However, do not make the figsize too big e. See show for full details. Note that the axes will not cross if the data is not on both sides of both axes, even if it is quite close:. Not all functions in Sage are symbolic. When plotting non-symbolic functions they should be wrapped in lambda :. Sage includes Matplotlib, which provides 2D plotting with an interface that is a likely very familiar to people doing numerical computation.

You can use plt. For example. We test that imshow works as well, verifying that trac ticket is fixed in Matplotlib. Since the above overwrites many Sage plotting functions, we reset the state of Sage, so that the examples below work!

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This matplotlib formatter selectively omits some tick values and passes the rest on to a specified formatter. The adaptive refinement algorithm for plotting a function f. See the docstring for plot for a description of the algorithm. Calculate plot points for a function f in the interval xrange. One can also name the array, and then use show or save :. It is possible to use figsize to change the size of the plot as a whole:.

Specifying only the number of rows or the number of columns computes the other dimension automatically:. The options like fontsizescale or frame passed to individual plots are preserved:. GraphicsArray for more examples. Doing so will plot nothing returning an empty plot. Note that if your list of complex numbers are all actually real, they get plotted as real values, so this.SageManifolds following styling of SageMath is an extension fully integrated into SageMathto be used as a package for differential geometry and tensor calculus.

The official page for the project is sagemanifolds. It can be used on CoCalc. SageManifolds deals with differentiable manifolds of arbitrary dimension. The basic objects are tensor fields and not tensor components in a given vector frame or coordinate chart.

In other words, various charts and frames can be introduced on the manifold and a given tensor field can have representations in each of them. An important class of treated manifolds is that of pseudo-Riemannian manifoldsamong which Riemannian manifolds and Lorentzian manifoldswith applications to General Relativity.

In particular, SageManifolds implements the computation of the Riemann curvature tensor and associated objects Ricci tensorWeyl tensor.

SageManifolds can also deal with generic affine connectionsnot necessarily Levi-Civita ones. This release propagates further code changes related to the integration of SageManifolds into SageMath cf.

More documentation is on doc. As SageMath is, SageManifolds is a free and open source software based on the Python programming language. To download and install SageManifolds, see here. Much of the source is on tickets at trac. There are Github repositories at github. Other links are provided at sagemanifolds. From Wikipedia, the free encyclopedia. This article does not cite any sources.

Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Categories : Free mathematics software Python scientific libraries Free software programmed in Python Free educational software Mathematical software. Hidden categories: Articles lacking sources from June All articles lacking sources.

Represent Graphs in SageMath

Namespaces Article Talk. Views Read Edit View history. Languages Add links. By using this site, you agree to the Terms of Use and Privacy Policy. Defined six classes, and "many doctests changed to comply with Sage 5. New methods in each class.

Development repository moved from svn to git. New example worksheets. More classes and methods some inherited from Sage. This is a major release, involving the introduction of algebraic structures to describe tensor fields, namely modules over the algebra of scalar fields, among which free modules of finite rank.Opened 11 years ago. Closed 8 years ago.

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Last modified 8 years ago. Depends on One workaround is to use matplotlib directly, with its semilogysemilogx and loglog functions, but that wouldn't produce plots with the customisations implemented in sage. Another workaround is messing with the plot figure like:. Also, this requires the user to know how to deal with figures, which is not directly exposed by sage. From what I noticed, Mathematica implements the separate functions way, but it may be better to fix the issue in plot itself and if the other functions are wanted, just make it so that they call plot with the correct arguments.

Download all attachments as:. This is a dupe if See for a way to solve this.

sagemath plot options

Since ended up just being about ticks not the scaledoesn't directly address how to change the scale of the plot. Here are some comments about an API. How about adding a show keyword that specifies the scale of the axes. We'd probably like some way to pass in arguments to the scale, since different scales have different options.

Sage Manifolds

I don't like using x and y, though, since the variables in the plot might not be x and y. Also, would appear to be slightly related. Integrating it with Graphics seemed quite a painful process, so I had to go this direction and make my own class. Currently, it handles many but not all of the arguments that the Graphics class supports. In addition it uses matplotlib.

In engineering, we often need logarithmic plots and the logarithmic plots sometimes is of the form that the x-axis decreases as we go towards the right for example if we plot decreasing probabilities on the x-axis.

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This LogGraphics takes this into account and makes sure that if a list of x-axis points with decreasing values along the higher indices of the list, then it plots the graph with a decreasing x-axis. The main thing it is lacking is that it doesn't inherit the Graphics class, and hence the set of plot options it supports is much less.

SageMath Plotting and Graphics

Since I needed to rewrite almost everything, I decided to just rewrite everything from scratch. Perhaps then it might be possible to integrate this patch better and consequently have access to all the methods and hence plot options available to the plot command. That said, it is IMHO better to have logarithmic plots as a separate class. For instance, it doesn't make much sense to "add" plots with different scalings and I also raise an error in the class I created.

It becomes impossible to add 2D and 3D graphics. It was a silly thing. I just needed to reorder the check for.

So, now it is possible to do this:. Actually most of the functions in sage. Using the log scale makes sense in only a couple of them though, and I have added some documentation and examples for the cases I think are pertinent. I think this should undergo a review now.

I hope to be able to go over this very valuable idea at the current Bug Days. Trivial comment while I'm doing a cursory read-through. Especially since the bulk of the "work" done in the code still happens in show and friends, I don't see why we couldn't just cherry-pick the keyword scale and handle it like we do things like plot tick formatting, separately from Graphics.Opened 8 years ago. Closed 4 years ago.

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However, if you want to choose different colors or linestyles for each function, then it seems you have to execute, e. It seems that the keyword 'fill' allows for a dictionary input, so perhaps the relevant code there could serve as a template?

Regarding the default coloring, please see also I like what is done in this ticket. One of the first things I tried after seeing automatic colors and plots, is try to enable legend labels. Would it be too hard to do so?

What is beyond my powers is to do a better job of picking colors; see comments 15 and 16 at I am fine with this ticket as it is. Let me know which approach you prefer. I have seen your comments in I agree that the colors could be chosen better, but that better be addressed in that ticket itself. Otherwise there will be too much overlap between the tickets and it will take ages to merge anything. I have a feeling that getting consensus on the automatic color spectrum will take some time and discussion since different people tend to like different things.

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Some are worried about how the colors will look - how much they can be differentiated - when printed in grayscale, while some others are more concerned about how they will look on the screen.

Not to mention accessibility issues - Jeroen, if you see this, do you have any particular thoughts from your perspective? Just be sure to check out some of the discussion here and regarding the auto -coloring options. I'm still somewhat reluctant to change the default due to accessibility and 'backwards compatibility' and that the yellow and a couple others are harder to seesince it's not like we are doing proper release notes and this may surprise some There was also discussion of whether rainbow is the best choice for multicolor for other reasons but I'll stay out of that.

Even a scale of different blues might be better than that. Karl-Dieter, since you appear to be the only developer disagreeing about having automatic colors, is there some way to solicit input on this question from users? Does Sage have some sort of user mailing list for sending out questions or making announcements of this sort?

What about an open question on ask. On matters of code, the doctests now pass but documentation building is still a problem, with at least two plots failing. Aaron, please try building the documentation to see where the errors are.

One feature that I do not like in this branch is that linestyle defaults to automatic. I find solid lines much easier to read and would prefer that linestyle default to solid.

That is in line with Mathematica behavior. Also, if both rgbcolor and color are specified, this branch silently overrides the former with the latter. In the current version of plot. I was in the future planning to remove that line and add code to raise a ValueError as Travis had me do in I think this branch should raise the ValueError rather than silently override an option, and then this decorator can be removed.

Usually in this case one of two things is done I don't think this is an "official" policy, though :. Sometimes it does matter enough, but even then usually on sage-devel only a few people will pipe up unless it's something that affects a fairly broad range of people. In this case, I don't care strongly enough to block this now that several people have 'officially' weighed in including on But in any case once it's decided here, you should close as a dup.

My 2 cents: I think having the default linestyle being a solid color is what we should do. Sorry, Travis, Not quite ready for reviewOpened 9 years ago. Closed 3 years ago. Recently there was a thread on the matplotlib list where someone posted matplotlib code for a streamline plot. It looks very nice. If the code doesn't get included in matplotlib, we could still ask about including it in Sage to do streamline plots.

Download all attachments as:. I've attached both code files so that we have them even if the above links go down for whatever reason. I'm not sure how to figure out which release it's in, if it's in a release yet. It looks like it will probably be in 1. Here is another example from somewhere in this discussion, allowing phase plots. Not directly related but looks nice with such things. I was hoping we could resurrect this ticket as I am teaching a class on ODE's this semester and would like to plot streamlines on top of the slope fields.

Does someone have some time to work on this? Alas, I don't know how much time I might have to do so. Since I spent too much time today reading graphics code, I can take a crack at this. It looks like a new class is needed, modeled on PlotField but calling the pyplot method streamplot instead of quiver.

It shouldn't be too difficult but won't happen overnight. Yes, this is exactly how you should do it. You could even keep it in the same module as the vector field plots, you can see that e. I agree with Karl-Dieter, you should definitely create a new class.

However, contour and density plots are in separate files.

sagemath plot options

This was surprisingly easy to get working! Then it was a matter of rearranging how the data arrays were assembled and changing the pyplot function name. Doctests and useful examples have been updated. Sorry to ask for a bit more. If this is too much trouble, I am okay with positive reviewing this ticket as-is. Travis, if by "initial point" you mean initial conditions, aren't those just part of the function arguments given to the plot?

What more do you intend with this feature? That one should stand alone, partly because the streamplot function it uses behaves differently from the quiver function used by the others. Would this convenience function be used regularly by others, or just you for one class?

What's the rule of thumb for adding those sorts of features to Sage?Opened 7 years ago. Closed 7 years ago. Last modified 7 years ago.

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Some cleaning there, and some doc, Download all attachments as:. Btw, I will try to deal with the pictures of our Belgian evening in Singapour sooner or later Yes, they are ugly.

But this acts like a global variable in the file. Also if and that's a big iflooking at my near future I get time, I will try to clean up some of the options in plotsso I would prefer there are less inconsistencies introduced in new patches! By the way that's a nice way to mention Singapore - it is really pouring all day long here! I am glad we agree on that. Patch updated, ugliness included. God I hate upper case variables.

And I hate standards even more. Replying to ncohen :. So if somebody feels like giving it a review :-P. I will update it in a couple of seconds to include Punarbasu's very sensible remark :-P.

sagemath plot options

Vincent : it seems to come from your patch How do you propose that we fix this? Oh, and there's something else that I would like to know. Does this decorator mean that in order to define a default option for two graphs, you made all Graph objects carry an additional dictionary? In the method in Arithgroup. The reason is that I want a nice picture with. Well, I guess that can be easily solved this way : would the "options" decorator work if you used it with empty parameters?

Something like that :.John Hunter Excellence in Plotting Contest submissions are open! Entries are due June 1, The optional parameter fmt is a convenient way for defining basic formatting like color, marker and linestyle. It's a shortcut string notation described in the Notes section below. You can use Line2D properties as keyword arguments for more control on the appearance. Line properties and fmt can be mixed. The following two calls yield identical results:.

There's a convenient way for plotting objects with labelled data i. Instead of giving the data in x and yyou can provide the object in the data parameter and just give the labels for x and y :. All indexable objects are supported. This could e. DataFame or a structured numpy array. The most straight forward way is just to call plot multiple times.

Alternatively, if your data is already a 2d array, you can pass it directly to xy. A separate data set will be drawn for every column. Example: an array a where the first column represents the x values and the other columns are the y columns:. The third way is to specify multiple sets of [x]y[fmt] groups:.

In this case, any additional keyword argument applies to all datasets. Also this syntax cannot be combined with the data parameter. By default, each line is assigned a different style specified by a 'style cycle'. The fmt and line property parameters are only necessary if you want explicit deviations from these defaults.

Alternatively, you can also change the style cycle using rcParams["axes. They can also be scalars, or two-dimensional in that case, the columns represent separate data sets. A format string, e.

See the Notes section for a full description of the format strings. Format strings are just an abbreviation for quickly setting basic line properties. All of these and more can also be controlled by keyword arguments. An object with labelled data.