Engineers: Stop Doing Algebra by Hand!
Save Time and Reduce Risk with Computer Algebra Systems
Manual equation manipulation is labor intensive, time consuming, and notoriously prone to error. Simply put, doing algebra by hand is expensive. When faced with expensive processes, engineers find ways to mechanize and cut costs. Math should be no different. Computer algebra systems automate the task of equation manipulation, reducing the need for human involvement and hence eliminate a source of risk. Pioneered originally by mathematicians and physicists, two trends have influenced their popularity with engineers.
Benefits of Computer Algebra Systems
Fewer Errors, and Faster than Manual Equation Manipulation
Manual equation manipulation requires intense cognitive effort. If that level of concentration is not maintained, errors will invariably pollute the equations. Computer algebra systems, however, eliminate the errors that invariably accompany manual equation manipulation, and are much faster. Additionally, removing the cognitive overhead associated with manual equation derivation enables engineers to concentrate on higher-level, higher-value tasks.
Model More Sophisticated Systems
As the size of engineering systems increase linearly, the size of the equations that describe those engineering systems increases exponentially. A key example is the modeling of multiple degree of freedom (DOF) robotic systems. As the number of joints increases, the transformation matrices required to describe joint motion exponentially increase in size. At some point, equation manipulation by hand is impractical; software support is hence needed. A corollary is that computer algebra systems can be used to model more sophisticated engineering systems than is possible by hand.
Computationally Faster than Numeric Computation
Numerical computation refers to the iterative solution of equations using software; this is computationally time-consuming. In many cases, computer algebra systems can be used to rearrange equations to an explicit formulation; this eliminates the need for time-consuming iterative approaches.
Preserve Information about Model Structure
By delaying numeric evaluation until only strictly necessary, computer algebra systems preserve information about model structure and parameter relationships. This information can be used for code generation, parameter-based optimization, model simplification and more.
Conclusion
The 1950s and 1960s saw the birth of the first computer algebra systems. Due to the skills and training of their creators, these innovative tools were first designed for the needs of mathematicians and physicists. Initially, a few forward-thinking engineers exploited symbolic math for advanced research applications. The benefits, however, remained out of reach for the vast majority of engineers. This started to change in the early eighties with the advent of cheap computing power. The next 30 years also saw the evolution of the human-centered design principles that radically improved the usability of computer algebra systems.
Moreover, a maturing feature set, including tools for managing calculations as well as doing calculations, made integrating mechanized algebra into the engineering design process much simpler. Computer algebra systems thus gradually entered the mainstream consciousness of engineers, and have grown in popularity year-on-year. Check out this white paper from Maplesoft which includes examples that clearly demonstrate the benefits of mechanized algebra across the entire breadth of engineering from balancing chemical equations to inverse kinematics.
This guest contribution is written by Samir Khan, Product Manager at Maplesoft. Maple by Maplesoft is a technical computing software for engineers, mathematicians, and scientists. Maple is available through the Altair Partner Alliance.
Manual equation manipulation is labor intensive, time consuming, and notoriously prone to error. Simply put, doing algebra by hand is expensive. When faced with expensive processes, engineers find ways to mechanize and cut costs. Math should be no different. Computer algebra systems automate the task of equation manipulation, reducing the need for human involvement and hence eliminate a source of risk. Pioneered originally by mathematicians and physicists, two trends have influenced their popularity with engineers.
- Human-centered design principles have vastly improved usability. Tasks such as equation manipulation, differentiation and ODE solving are now much easier to do, reducing the need for specialized training.
- Computer algebra systems now also offer tools for numerical math, plotting, connectivity, data analysis, documentation and deployment. This means that algebraic computations can be fully integrated into the entire engineering design process.
Benefits of Computer Algebra Systems
Fewer Errors, and Faster than Manual Equation Manipulation
Manual equation manipulation requires intense cognitive effort. If that level of concentration is not maintained, errors will invariably pollute the equations. Computer algebra systems, however, eliminate the errors that invariably accompany manual equation manipulation, and are much faster. Additionally, removing the cognitive overhead associated with manual equation derivation enables engineers to concentrate on higher-level, higher-value tasks.
Model More Sophisticated Systems
As the size of engineering systems increase linearly, the size of the equations that describe those engineering systems increases exponentially. A key example is the modeling of multiple degree of freedom (DOF) robotic systems. As the number of joints increases, the transformation matrices required to describe joint motion exponentially increase in size. At some point, equation manipulation by hand is impractical; software support is hence needed. A corollary is that computer algebra systems can be used to model more sophisticated engineering systems than is possible by hand.
Computationally Faster than Numeric Computation
Numerical computation refers to the iterative solution of equations using software; this is computationally time-consuming. In many cases, computer algebra systems can be used to rearrange equations to an explicit formulation; this eliminates the need for time-consuming iterative approaches.
Preserve Information about Model Structure
By delaying numeric evaluation until only strictly necessary, computer algebra systems preserve information about model structure and parameter relationships. This information can be used for code generation, parameter-based optimization, model simplification and more.
Conclusion
The 1950s and 1960s saw the birth of the first computer algebra systems. Due to the skills and training of their creators, these innovative tools were first designed for the needs of mathematicians and physicists. Initially, a few forward-thinking engineers exploited symbolic math for advanced research applications. The benefits, however, remained out of reach for the vast majority of engineers. This started to change in the early eighties with the advent of cheap computing power. The next 30 years also saw the evolution of the human-centered design principles that radically improved the usability of computer algebra systems.
Moreover, a maturing feature set, including tools for managing calculations as well as doing calculations, made integrating mechanized algebra into the engineering design process much simpler. Computer algebra systems thus gradually entered the mainstream consciousness of engineers, and have grown in popularity year-on-year. Check out this white paper from Maplesoft which includes examples that clearly demonstrate the benefits of mechanized algebra across the entire breadth of engineering from balancing chemical equations to inverse kinematics.
This guest contribution is written by Samir Khan, Product Manager at Maplesoft. Maple by Maplesoft is a technical computing software for engineers, mathematicians, and scientists. Maple is available through the Altair Partner Alliance.
