Differences Between the Legacy and New Symbolic Engines
The new symbolic engine introduced in PTC Mathcad Prime 6.0.0.0 replaces the legacy symbolic engine in previous releases. While in PTC Mathcad Prime 6.0.0.0 you could switch between the legacy and the new symbolic engines, starting with PTC Mathcad Prime 7.0.0.0, the new symbolic engine is the only one available. The differences between the legacy and the new engines are listed below:
Appearance Differences
• Order of arguments in the results
The legacy symbolic engine returns the resulting expression as-is. The new symbolic engine returns the result in the correct mathematical order.
Figure 1. Legacy Symbolic Engine
Figure 2. New Symbolic Engine
• Results are formulated differently
After symbolic evaluation, the legacy symbolic engine returns the result without any rearrangements. The new symbolic engine returns the expression in an easy-to-read arrangement.
Figure 3. Legacy Symbolic Engine
Figure 4. New Symbolic Engine
• Normalization of floating-point numbers in exponential notation
The legacy symbolic engine returns a non-zero first digit. The new symbolic engine returns a zero first digit. The legacy symbolic engine normalizes mantissa of a non-zero number to [1.0,10.0]. The new symbolic engine normalizes mantissa to [0.1, 1.0].
Figure 5. Legacy Symbolic Engine
Figure 6. New Symbolic Engine
• Rounding of floating-point numbers
The legacy symbolic engine rounds 0.5 to 0. The new symbolic engine rounds off 0.5 to 1.
Figure 7. Legacy Symbolic Engine
Figure 8. New Symbolic Engine
• Simplification of double minus
In a few cases, the legacy symbolic engine returns results with a double minus. The new symbolic engine simplifies the result and returns a plus sign.
Figure 9. Legacy Symbolic Engine
Figure 10. New Symbolic Engine
• Formatting of answers
The new symbolic engine returns more readable answers.
◦ Example 1:
Figure 11. Legacy Symbolic Engine
Figure 12. New Symbolic Engine
◦ Example 2:
Figure 13. Legacy Symbolic Engine
Figure 14. New Symbolic Engine
Evaluation Differences
• Handling of floating-point arguments
Even when one argument is a floating-point number, the new symbolic engine assumes all the arguments to be floating-point numbers and returns a numeric floating-point result.
Figure 15. Legacy Symbolic Engine
Figure 16. New Symbolic Engine
• Improved rewrite support
The legacy symbolic engine calculates the result and replaces the terms in initial expression. The new symbolic engine applies additional simplification and returns a simplified result.
 | To replace the resulting terms in the initial expression as in the legacy symbolic engine, use modifier raw. |
Figure 17. Legacy Symbolic Engine
Figure 18. New Symbolic Engine
• Arbitrary precision math
The legacy symbolic engine limits the numeric result to 250 digits. The new symbolic engine does not have a numeric limit.
| | The higher the numeric limit, the longer it takes to calculate the result. |
Figure 19. Legacy Symbolic Engine
Figure 20. New Symbolic Engine
• Variable domain assumption
The legacy symbolic engine assums undefined free variables as complex. The new symbolic engine assumes undefined free variables as real. Using keyword assume with modifiers real and complex helps calculate the desired result. Keyword assume with modifier complex must not be used to force complex domain assumption.
Figure 21. Legacy Symbolic Engine
Figure 22. New Symbolic Engine
• Different strategy in simplification of fractions
The legacy symbolic engine separates large fractions into an expression with several simpler fractions. The new symbolic engine finds a common denominator and returns result as a large fraction. To get the result in a simpler form, use keyword simplify.
Figure 23. Legacy Symbolic Engine
Figure 24. New Symbolic Engine
• Corrections in behavior of functions
The new symbolic engine corrects the behavior of some functions which now work in accordance with help definition and build-in numeric.
◦ Example 1:
Figure 25. Legacy Symbolic Engine
Figure 26. New Symbolic Engine
◦ Example 2:
Figure 27. Legacy Symbolic Engine
Figure 28. New Symbolic Engine
• Improved support for keyword solve
◦ Linear inequality with complex coefficients
In case of inequalities, the legacy symbolic engine returns only real answers and errors in other cases. The new symbolic engine returns results with real and complex components.
▪ Example 1:
Figure 29. Legacy Symbolic Engine
Figure 30. New Symbolic Engine
▪ Example 2:
Figure 31. Legacy Symbolic Engine
Figure 32. New Symbolic Engine
▪ Example 3:
Figure 33. Legacy Symbolic Engine
Figure 34. New Symbolic Engine
▪ Example 4:
Figure 35. Legacy Symbolic Engine
Figure 36. New Symbolic Engine
▪ Example 5:
Figure 37. Legacy Symbolic Engine
Figure 38. New Symbolic Engine
◦ Improved evaluation of system of inequalities
The new symbolic engine returns the correct range, where the solution is defined.
Figure 39. Legacy Symbolic Engine
Figure 40. New Symbolic Engine
◦ Calculation time
The legacy symbolic engine takes longer evaluation time. The new symbolic engine returns results faster.
Figure 41. Legacy Symbolic Engine
Figure 42. New Symbolic Engine
• Float limit values
The legacy symbolic engine does not support the summation and multiplication using floats in variables and is inconsistent with numeric evaluations. The new symbolic engine supports these features.
◦ Example 1:
Figure 43. Legacy Symbolic Engine
Figure 44. New Symbolic Engine
◦ Example 2:
Figure 45. Legacy Symbolic Engine
Figure 46. New Symbolic Engine
◦ Example 3:
Figure 47. Legacy Symbolic Engine
Figure 48. New Symbolic Engine
◦ Example 4:
Figure 49. Legacy Symbolic Engine
Figure 50. New Symbolic Engine
• Improved sorting function
With the legacy symbolic engine, sorting function return an error. In the new symbolic engine, sorting functions return the correct result.
◦ Example 1:
Figure 51. Expression
Figure 52. Legacy Symbolic Engine
Figure 53. New Symbolic Engine
◦ Example 2:
Figure 54. Expression
Figure 55. Legacy Symbolic Engine
Figure 56. New Symbolic Engine
• Solved transformations support
The legacy symbolic engine returns a general formula for unsolved transformations. The new symbolic engine returns solved transformations.
◦ Example 1:
Figure 57. Legacy Symbolic Engine
Figure 58. New Symbolic Engine
◦ Example 2:
Figure 59. Legacy Symbolic Engine
Figure 60. New Symbolic Engine
• Keyword substitute
The new symbolic engine provides improved support for keyword substitute.
◦ Example 1:
Figure 61. Legacy Symbolic Engine
Figure 62. New Symbolic Engine
◦ Example 2:
Figure 63. Legacy Symbolic Engine
Figure 64. New Symbolic Engine
◦ Example 3:
Figure 65. Legacy Symbolic Engine
Figure 66. New Symbolic Engine
◦ Example 4:
Figure 67. Legacy Symbolic Engine
Figure 68. New Symbolic Engine
• Support for prime notations
The new symbolic engine provides improved implementation of prime notations.
Figure 69. Expression
Figure 70. Legacy Symbolic Engine
Figure 71. New Symbolic Engine
• Square matrix logarithm calculation
The new symbolic engine calculates the logarithm of square matrix. The legacy symbolic engine does not support this functionality.
Figure 72. Expression
Figure 73. Legacy Symbolic Engine
Figure 74. New Symbolic Engine
• Min/max function support
The new symbolic engine provides fixed support for min/max functions. The legacy symbolic engine does not support this functionality.
◦ Example 1:
Figure 75. Legacy Symbolic Engine
Figure 76. New Symbolic Engine
◦ Example 2:
Figure 77. Legacy Symbolic Engine
Figure 78. New Symbolic Engine
