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Expression of type Lambda

from the theory of proveit.linear_algebra.addition

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, Lambda, N, k, vk
from proveit.linear_algebra import ScalarMult
from proveit.logic import InSet
from proveit.numbers import Exp, Interval, Mult, e, i, one, pi, two
In [2]:
# build up the expression from sub-expressions
expr = Lambda(k, Conditional(ScalarMult(Exp(e, Mult(two, pi, i, k)), vk), InSet(k, Interval(one, N))))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
k \mapsto \left\{\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot k} \cdot v\left(k\right) \textrm{ if } k \in \{1~\ldotp \ldotp~N\}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 26
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 5
3Operationoperator: 6
operands: 7
4Literal
5ExprTuple8, 9
6Literal
7ExprTuple26, 10
8Operationoperator: 11
operands: 12
9Operationoperator: 13
operand: 26
10Operationoperator: 15
operands: 16
11Literal
12ExprTuple17, 18
13Variable
14ExprTuple26
15Literal
16ExprTuple19, 20
17Literal
18Operationoperator: 21
operands: 22
19Literal
20Variable
21Literal
22ExprTuple23, 24, 25, 26
23Literal
24Literal
25Literal
26Variable