PolymathPlus
PolymathPlus

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 user-friendly Math Solver.

The PolymathPlus solver is available as a web application or a Windows desktop application. A link to the online solver becomes visible on the left menubar after login. We are encouraging users to switch to the online version while keeping support for the Windows desktop application for paid licenses.

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

### News

Version 7.0.46 (from Feb 14, 2024) has the following key changes:
 ✅ The student license has been upgraded to support up to 50 explicit auxiliary equations ✅ Support for a very large number of ODEs (over 1,000) for professional licenses ✅ A new numerical integration method for experimental data points has been introduced

# 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 tf=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.

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

PolymathPlus Syntax Fit Description Curve to Fit
polyfit x y 1 Linear regression y = a0 + a1x
polyfit x y 1 origin Linear regression via origin y = a1x
polyfit x y 2 Polynomial regression 2nd order y = a0 + a1x + a2x2

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.

# Linear regression example # Straight line fit for BOD vs Time data [ 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

### Program Settings and Hints

PolymathPlus enables users to customize the format of solution reports and the selection of algorithms using hints. These hints are stored within the PolymathPlus program file and are prefixed with #@.

The sample program below includes several hint lines, used to modify the number of digits displayed in the report, adjust the size and content of the chart, and display a table of intermediate data points in the solution report.

# Example ODE System solution with custom # hints for the solution report format #@Report_fix_digits = 12 #@Chart_Size = 400; 250 #@Chart_Y_Curves = T2 T3 #@Report_Show_Intermediate_data_points = yes #@DEQ_Intermediate_data_points = 30 #@Report_show_Settings = yes d(T1)/d(t)=(W*Cp*(T0-T1)+UA*(Tsteam-T1))/(M*Cp) d(T2)/d(t)=(W*Cp*(T1-T2)+UA*(Tsteam-T2))/(M*Cp) d(T3)/d(t)=(W*Cp*(T2-T3)+UA*(Tsteam-T3))/(M*Cp) W=100 Cp=2.0 T0=20 UA=10. Tsteam=250 M=1000 t(0)=0 T1(0)=20 T2(0)=20 T3(0)=20 t(f)=200

More examples can be found in the Sample Library.

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.

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.

This section pertains to organizations purchasing bulk licenses, who may also intend to utilize PolymathPlus on their public lab computers. To view or renew the site license, please access the site admin page using the form below. The site's admin page also contains information on how to distribute the software and the keys users will need to claim the advanced features.

### 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 College123 University AvenueCollege Town, CA 98765United States

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

# Sample Library

#### Simon

The boss of all bosses

### Nonlinear Regression

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 (compared to the individual license costs).
 Site License Annual Cost Student \$370 per 50 users \$450 per 100 users Pro \$1250 per 50 users \$1500 per 100 users

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

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.
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.
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 10 50 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

The online version of PolymathPlus has several advantages over the traditional desktop version. We advocate using it for the following reasons:

• 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:

1. What is PolymathPlus?
2. Is PolymathPlus free?
3. Can I use PolymathPlus from my Windows/Mac laptop?
4. How can I try the online solver?
5. What type of licenses does PolymathPlus offer?
6. Which mathematical algorithms does PolymathPlus use?
7. What is the history of PolymathPlus?
8. Does PolymathPlus offer a desktop version package?
9. What is the user profile page?
10. What is the 'Site Admin' page, and who can use it?
11. I am interested in procuring a site license for my organization. What steps should I take?
12. How can I link my existing account to a site license my organization purchased?
13. Desktop application fails with WebView2 controllers compatibility
14. Troubleshooting: Too many steps in routine or step size underflow
15. Troubleshooting: LNSRCH: Roundoff problem in lnsrch
16. How can I support PolymathPlus?

PolymathPlus 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 DistrictTbilisi 0101Georgia Email admin@polymathplus.org sales@polymathplus.org US Phone +1 530 405 9303 Pre-scheduled calls: 08:00-10:00 AM ET Availability Status Maintenance Status

The development of our software had been encouraged by:

• CACHE The Computer Aids for Chemical Engineering Education Corporation, as part of the
• AIChE The American Institute of Chemical Engineers

Drawing from more than 25 years of software development and extensive research in numerical packages, we have crafted the new PolymathPlus package.

Our new organization has its foundation in Georgia, Tbilisi. Our office, though modest, serves as a hub for our dedicated staff. We maintain ties with many US-based universities and others worldwide.

## 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.