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diffalg[leader] - return the leader of a differential polynomial
diffalg[rank] - return the rank of a differential polynomial
diffalg[initial] - return the initial of a differential polynomial
diffalg[separant] - return the separant of a differential polynomial
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Calling Sequence
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leader (q, R)
rank (q, R)
initial (q, R)
separant (q, R)
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Parameters
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q
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differential polynomial
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R
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differential polynomial ring
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Description
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The leader of a differential polynomial q is the greatest derivative occurring in q with respect to the ranking of R.
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The rank of q is the leader of q raised to the degree of q with respect to its leader.
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The initial of q is the leading coefficient of q with respect to its leader.
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The separant of q is the partial derivative of q with respect to its leader. It is also the initial of any proper derivative of q.
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If q belongs to the ground field R, then leader, rank, initial and separant return an error message.
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The command with(diffalg,leader) allows the use of the abbreviated form of this command.
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The command with(diffalg,rank) allows the use of the abbreviated form of this command.
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The command with(diffalg,initial) allows the use of the abbreviated form of this command.
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The command with(diffalg,separant) allows the use of the abbreviated form of this command.
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Examples
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Important: The diffalg package has been deprecated. Use the superseding package DifferentialAlgebra instead.
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![R := differential_ring(derivations = [t], ranking = [u])](/support/helpjp/helpview.aspx?si=7145/file07264/math168.png)
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| (1) |
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![p := (u[t]-1)*u[t, t]^2+u[t, t]+u[t]^2+t*u[]](/support/helpjp/helpview.aspx?si=7145/file07264/math175.png)
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![p := (u[t]-1)*u[t, t]^2+u[t, t]+u[t]^2+t*u[]](/support/helpjp/helpview.aspx?si=7145/file07264/math178.png)
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![u[t, t]](/support/helpjp/helpview.aspx?si=7145/file07264/math185.png)
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![u[t, t]^2](/support/helpjp/helpview.aspx?si=7145/file07264/math192.png)
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![u[t]-1](/support/helpjp/helpview.aspx?si=7145/file07264/math199.png)
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![2*u[t, t]*u[t]-2*u[t, t]+1](/support/helpjp/helpview.aspx?si=7145/file07264/math206.png)
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![K := field_extension(transcendental_elements = [a, b])](/support/helpjp/helpview.aspx?si=7145/file07264/math212.png)
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![R := differential_ring(field_of_constants = K, derivations = [t], ranking = [u])](/support/helpjp/helpview.aspx?si=7145/file07264/math216.png)
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| (7) |
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![p := 2*u[t]*b*u[t, t]^2+u[]*u[t, t]^2/a+u[t]](/support/helpjp/helpview.aspx?si=7145/file07264/math223.png)
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![p := 2*u[t]*b*u[t, t]^2+u[]*u[t, t]^2/a+u[t]](/support/helpjp/helpview.aspx?si=7145/file07264/math226.png)
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![(2*u[t]*b*a+u[])/a](/support/helpjp/helpview.aspx?si=7145/file07264/math233.png)
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![u[t, t]](/support/helpjp/helpview.aspx?si=7145/file07264/math240.png)
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![u[t, t]^2](/support/helpjp/helpview.aspx?si=7145/file07264/math247.png)
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![(2*u[t]*b*a+u[])/a](/support/helpjp/helpview.aspx?si=7145/file07264/math254.png)
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![(4*u[t]*b*u[t, t]*a+2*u[]*u[t, t])/a](/support/helpjp/helpview.aspx?si=7145/file07264/math261.png)
| (13) |
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![p := u[x, y]*v[x, y, y]^2+u[x, x]^2+u[x]](/support/helpjp/helpview.aspx?si=7145/file07264/math267.png)
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![p := u[x, y]*v[x, y, y]^2+u[x, x]^2+u[x]](/support/helpjp/helpview.aspx?si=7145/file07264/math270.png)
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![R1 := differential_ring(derivations = [x, y], ranking = [u, v])](/support/helpjp/helpview.aspx?si=7145/file07264/math274.png)
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![u[x, x]](/support/helpjp/helpview.aspx?si=7145/file07264/math284.png)
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![u[x, x]^2](/support/helpjp/helpview.aspx?si=7145/file07264/math291.png)
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| (18) |
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![2*u[x, x]](/support/helpjp/helpview.aspx?si=7145/file07264/math305.png)
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![2*u[x, x]](/support/helpjp/helpview.aspx?si=7145/file07264/math312.png)
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![R2 := differential_ring(derivations = [x, y], ranking = [[u, v]])](/support/helpjp/helpview.aspx?si=7145/file07264/math316.png)
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![v[x, y, y]](/support/helpjp/helpview.aspx?si=7145/file07264/math326.png)
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![v[x, y, y]^2](/support/helpjp/helpview.aspx?si=7145/file07264/math333.png)
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![u[x, y]](/support/helpjp/helpview.aspx?si=7145/file07264/math340.png)
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![2*v[x, y, y]*u[x, y]](/support/helpjp/helpview.aspx?si=7145/file07264/math347.png)
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![2*v[x, y, y]*u[x, y]](/support/helpjp/helpview.aspx?si=7145/file07264/math354.png)
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See Also
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diffalg(deprecated), diffalg(deprecated)/differential_algebra, diffalg(deprecated)/differential_ring, diffalg(deprecated)/field_extension, diffalg(deprecated)[differentiate], DifferentialAlgebra[Tools][Get], DifferentialAlgebra[Tools][Initial], DifferentialAlgebra[Tools][LeadingCoefficient], DifferentialAlgebra[Tools][LeadingDerivative], DifferentialAlgebra[Tools][LeadingRank], DifferentialAlgebra[Tools][Separant]
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