Approximately equal symbol maple9/15/2023 ![]() ![]() International shortcut keys are provided for users whose keyboard layouts do not handle the existing keys.įor international shortcut keys on Mac, it is possible to use Opt instead of Alt. Greek Mode (Next Character Entered as Greek)Ĭtrl + Shift + G ( Command + Shift + G, for Mac)Įscape Next Character (For displaying "^" or "_", for example)Ĭtrl + Alt + K ( Command + Alt + K, for Mac)Ĭtrl + Alt + J ( Command + Alt + J, for Mac)Ĭtrl + Alt + L ( Command + Alt + L, for Mac)ġ Use right arrow key to leave denominator, numerator, superscript, or subscript region. Place the cursor on the last row, and press the shortcut keys.Ĭtrl + Shift + C ( Command + Shift + C, for Mac)Ĭtrl + Shift + ^ ( Command + Shift + ^, for Mac)Ĭtrl + Alt + P ( Command + Alt + P, for Mac) Note: To increase the size of a piecewise function, add a new row. New Row in Matrix, Vector, or a Piecewise ExpressionĬtrl + Shift + R ( Command + Shift + R, for Mac) Nthroot and then command/symbol completion Literal Subscript 1 (Subscripted Variable Name)Ĭtrl + Shift + A ( Command + Shift + A, for Mac)Ĭtrl + Alt + U ( Command + Alt + U, for Mac)Ĭtrl + Shift + " ( Command + Shift + ", for Mac)Ĭtrl + Alt + O ( Command + Alt + O, for Mac) Indexed Subscript versus Literal SubscriptĮvaluate and Display Inline (Document Mode)Ĭtrl + Shift + _ ( Command + Shift + _, for Mac)Ĭtrl + Alt + B ( Command + Alt + B, for Mac) Escaping Characters that are Shortcut KeysĮntering Derivatives Using Prime Notation and Dot Notation The force option was introduced in Maple 2022.įor more information on Maple 2022 changes, see Updates in Maple 2022. The MultivariatePowerSeries command was updated in Maple 2022. The MultivariatePowerSeries command was introduced in Maple 2021.įor more information on Maple 2021 changes, see Updates in Maple 2021. We can use the force option to make Maple do the actual comparisons.ĪpproximatelyEqual f, g, 10, force In this case, the analytic expressions for the coefficients are all pairwise equal. G ≔ UnivariatePolynomialOverPowerSeries PowerSeries 0, Inverse PowerSeries 1 − x − y, z :ĪpproximatelyEqual f, g, 10 The coefficient of z is also the same, even though this is not immediately obvious from their definition.į ≔ UnivariatePolynomialOverPowerSeries PowerSeries 0, GeometricSeries x, y, z : We define two univariate polynomials over power series, both linear in their with main variable z. ![]() In order to test this, we needed to compute the terms of homogeneous degree 2, as we can see by calling Truncate again. However, the homogeneous degree 2 parts of a and c are different.ĪpproximatelyEqual a, c, 2 As we see above, these are the same for a and c but different for b. The power series a, b, and c all have the terms up to homogeneous degree 1 computed. Two power series p and q are said to be equal up to a degree deg, called the precision, if for each degree d Ī ≔ Inverse PowerSeries 1 + x + yĪ ≔ Pow&ExponentialE rS&ExponentialE rⅈ&ExponentialE s of 1 1 + x + y : 1 + …Ĭompute its linear truncation with the Truncate command.ī ≔ Pow&ExponentialE rS&ExponentialE rⅈ&ExponentialE s of 1 1 − x − y : 1 + x + y + …Ĭ ≔ Inverse SumOfAllMonomials x, yĬ ≔ Pow&ExponentialE rS&ExponentialE rⅈ&ExponentialE s of 1 − x 1 − y : 1 + … (optional) the keyword option force or force = true or force = false (optional) the precision up to which to compare the inputs Univariate polynomials over power series generated by this package ![]()
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