Polymath^Plus

Math-Solver for Students, Scientists, and Engineers
⬤ Enter a problem in plain text ▶ Press the Solve button ⬤ Get a numeric solution

Linear Equations	Nonlinear Equations
Differential Equations	Curve Fitting Regression

Embracing our vision, we offer a vibrant, free version of our premier user-friendly Math Solver.

The Polymath^Plus solver is available as a web application. A link to the solver becomes visible on the left menubar after login. We are encouraging users to switch to the online version while gradually phasing out support for the Windows desktop application.

Our internal algorithms have been extensively used over the years by many engineering faculties in universities across the world. Students and professionals will appreciate the ease of use and the comprehensive solution reports of our application.

Supported Web Browsers

Chrome	85	Safari	14
Edge	85	Firefox	79
Opera	71

Modules

Linear Equations

PolymathPlus can solve linear equations of any size. The number of equations should be equal to the number of unknown linear variables. Here's an example of 3 linear equations to be solved simultaneously:

Below are the equations entered into the PolymathPlus problem input text box (note that the # sign indicates user remarks and is being ignored by the program):

# linear equations a + 2*c = 50 b = -2 + c a + 23*c = 12 + b

Nonlinear Equations

When solving simultaneous nonlinear equations, the equations have to be written as root expressions (expressions that are equal to zero in the solution). In addition, an initial guess should be provided for each nonlinear variable.
Below is a sample problem and data entry for solving 2 nonlinear equations:

When entering the problem into PolymathPlus, we should enter the root expressions, each associated to a nonlinear variable function. We should also provide an initial estimate for each nonlinear variable. In the example below, we have 2 nonlinear variables x and y, hence 2 root functions, and we provide an initial guess of 1 for both x, and y.

f(x) = x^2 + y - 12 f(y) = 2*x + log(y+2) - 5 x(0)=1 y(0)=1

Note that we may also define any number of auxiliary expressions, to simplify long expressions, in this example we define a as an auxiliary expression:

f(x) = x^2 + y - 12 f(y) = 2*x + a a = log(y+2) - 5 x(0)=1 y(0)=1

In case we only have one nonlinear equation to solve (with any number of auxiliary expressions), we need to provide a min/max estimates for the nonlinear variable. For example, below is a PolymathPlus program for solving one nonlinear equation where we need to evaluate V:

f(V) = (P+a/(V^2))*(V-b)-R*T P=56 R=0.08206 T=450 Tc=405.5 Pc=111.3 Pr=P/Pc a=27*(R^2*Tc^2/Pc)/64 b=R*Tc/(8*Pc) Z=P*V/(R*T) V(min)=0.4 V(max)=1

Differential Equations

Entering and solving ordinary differential equations with PolymatPlus is simple.
Consider this set of equations to be solved:

Given the initial conditions x₀=1, y₀=4, at t₀=0, and having the integration finish at t_f=1,
the text below should be entered into PolymathPlus:

x' = x + 4*t^2 y' = sqrt(y) - x/(5-y) x|1 y|4 t|0:1

The following alternative compatible syntax can also be used for the same problem:

d(x)/d(t) = x + 4*t^2 d(y)/d(t) = sqrt(y) - x/(5-y) x(0)=1 y(0)=4 t(0)=0 t(f)=1

The solution will be displayed in a tabular format and will also include the integration chart:

Curve Fitting

PolymathPlus supports curve fitting for polynomial, multi-linear, and nonlinear regression. The report evaluates the model variables, generates a regression chart, residual plots, and provides statistics on the accuracy of the model.

Here is an example of the data entry required for solving a linear regression model for a given set of data points.
We solve a polynomial regression model with the order of 1 (hence linear regression) which best fits the linear equation matching the given data points.

polyfit <x> <y> <order> [origin]

# Linear regression example # Straight line fit to BOD data # BOD = a0 + a1*Time [ t BOD 1 0.6 2 0.7 4 1.5 6 1.9 8 2.1 10 2.6 12 2.9 14 3.7 16 3.5 18 3.7 20 3.8 ] Time = t + 10 polyfit Time BOD 1

Below is an example of a data entry for solving nonlinear regression model for a given set of data points. The model variables to be found are a and b, for which we should also provide an initial guess.

# Example: Nonlinear Regression [ x y g 0.5 1.255 1.2 0.387 1.25 1.3 0.24 1.189 1.4 0.136 1.124 2.0 0.04 0.783 2.1 0.011 0.402 2.2 ] # Nonlinear regression model nlinfit y = a * x / (b + x) # Initial guess of the # regression model variables a,b m(a)= 2 m(b)= 1

More examples can be found in this Help file.

Register

Access to the online solver requires users to be registered and logged in. Once logged in, users can access the online solver.
If you're a new user, please fill out the form below to register and gain login access.

Email Address

Full Name

Academics Industry/Other

I have read and agree to the Terms of Service (TOS)

Please don't use the form above to register the application on a public or cloud computers, site IT administrators should get a site registration license instead.
For private desktop installation registration please enter the username on the Name field, and the computer name on the Organization field.

Site License Admin Access

This section pertains to organizations purchasing bulk licenses, who may also intend to utilize Polymath^Plus on their public lab computers. To view or renew the site license, please access the site admin page using the form below.

IT Access Form

To initiate the registration of a new site, please reach out to us and provide the following details:

	Detail	Example
1.	Site name	Arizona State University
2.	IT contact email	john123@asu.edu
3.	Backup email	abra2759@asu.edu
4.	Email extension/s	@asu.edu, @student.asu.edu
5.	Site Address	ABC College 123 University Avenue College Town, CA 98765 United States

Then, we will provide an access key with which you can get invoices, purchase licenses, and read the proliferation instructions.

Sample Library

Linear and Explicit Equations

Nonlinear Equations

Differential Equations

Linear/Polynomial Regression

Multilinear Regression

Nonlinear Regression

Licenses

Site Licenses

We are pleased to announce that we will be offering new site licenses for PolymathPlus. These licenses are designed for institutions and organizations that require multiple-user access to our software. With a site license, you will have the flexibility to purchase a bulk quantity of either student or professional licenses, such as 100 student licenses for a site. Designated site administrators will have online management capabilities through the Site Admin page. For example, they will be provided with a unique activation key for both the online program and the desktop application.

Site licenses will be sold in bulk quantities of 50 licenses at a 50% discount or 100 licenses at a 70% discount.

Site License	Annual Cost
Student	$370	per 50 users
Student	$450	per 100 users
Pro	$1250	per 50 users
Pro	$1500	per 100 users

Institutions with site licenses may continue to install the desktop version on their public computers. Additional details are available on the Site Admin page.

Individual Licenses

We are pleased to offer the following individual user license types:

Free

This license will enable users to access a curated set of features that encompass a wide range of functionalities. We believe it is important to provide an accessible version of our software for individuals who may have limited resources or are new to mathematical modeling. As its name suggests, all registered users are automatically granted a free license, enabling them to use the online PolymathPlus web application.

Student

Designed specifically for students, this license offers a comprehensive set of features at an affordable price. With the student license, users will have access to advanced mathematical tools and functions, making it an ideal choice for educational purposes.

Pro

Tailored to meet the needs of professionals and researchers, the professional license provides the complete range of features and capabilities offered by PolymathPlus. This license is priced accordingly to support ongoing product development and customer support.

The following table lists program capacities and features per license.

Capacity & Features	Free	Std	Pro
Lines of code	50	200	∞
Program file size	1KB	10KB	∞
Online saved programs	5	100	∞
Nonlinear equations	5	10	100
Differential equations	5	10	2000
Supporting auxiliary variables	5	20	2000
Regression data points	20	100	∞
Regression model variables	5	10	∞
Intermediate data points table	50	300	1000
Solver requests per month	100	∞	∞
Online solver	✅	✅	✅
Windows desktop application		✅	✅
Dynamic charts		✅	✅
Advanced tools ie. Latex			✅
Annual Cost sales tax included (USD)	Free	$15	$50

   ∞ Maximized within reasonable resource limits.
   ✱ Users who registered for PolymathPlus before August 28, 2023, will maintain their full access until Jan 2024.
   ✱ The Windows desktop application will be available for Std/Pro licenses during October 2023 following a formal announcement.

Users can purchase individual licenses through their online profile page.

Online and Desktop Programs

We understand that you have been utilizing either or both the online and desktop versions of PolymathPlus, and we would like to emphasize some advantages of the online version:

Accessibility: The online version allows users to access the software from any device with internet connectivity, eliminating the need for software installations and updates.
Cross-Platform Compatibility: Our online version is compatible with various operating systems and devices, i.e. Windows, macOS, Linux, Android, and iOS, providing users a seamless experience across platforms.
Collaboration and Sharing: With the online version, users can easily collaborate with peers, share calculations, and work on projects collectively. This fosters a sense of community and encourages knowledge exchange among users.

Development of the desktop version will be slowed down until we secure adequate funds to align it with our online version.

Q&A

Click any question below for an answer:

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1. What is PolymathPlus?

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2. Is PolymathPlus free?

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3. Can I use PolymathPlus from my Windows/Mac laptop?

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4. How can I try the online solver?

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5. What type of licenses does PolymathPlus offer?

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6. Which mathematical algorithms does PolymathPlus use?

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7. What is the history of PolymathPlus and who are its members?

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8. Does PolymathPlus offer a desktop version package?

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9. What is the user profile page?

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10. What is the 'Site Admin' page, and who can use it?

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11. I am interested in procuring a site license for my organization. What steps should I take?

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12. How can I link my existing account to a site license my organization purchased?

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13. How can I support PolymathPlus?

About Us

Polymath^Plus began as a Windows desktop application and expanded its offerings to include an online web application. Our passion and dedication drive us to continually innovate and refine our solutions. We are committed to providing a top-notch numerical solver package to tackle mathematical challenges with ease and confidence.

We have recently initiated a new operation in the picturesque region of Georgia. With high hopes and aspirations, we aim to expand our reach and make a more significant and positive impact on the academic and scientific communities.

Firm Name	PLMT Plus LLC
Legal Address	Otar Kinkladze Street, N39 Chughureti District Tbilisi 0101 Georgia
Admin Email	admin@polymathplus.org
Sales Email	sales@polymathplus.org
Phone	+995595490920

Our Vision

Deliver the world's premier, user-friendly, yet advanced math solver, accessible and affordable for users worldwide, empowering learners, professionals, and enthusiasts to confidently conquer mathematical challenges.

Terms and Conditions

PolymathPlus does not warrant that the functions contained in the program will meet your requirements or that the operation of the program will be uninterrupted or error-free. In no event will PolymathPlus or its distributors or their dealers be liable to you for any damages, including any lost profit, lost savings, lost patience, or other incidental or consequential damage.
Please carefully read the terms of service indicated in the link below.

Terms of Service (TOS)