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Expression of type Conditional

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, 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 = 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())
\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()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operands: 4
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7, 8
5Literal
6ExprTuple25, 9
7Operationoperator: 10
operands: 11
8Operationoperator: 12
operand: 25
9Operationoperator: 14
operands: 15
10Literal
11ExprTuple16, 17
12Variable
13ExprTuple25
14Literal
15ExprTuple18, 19
16Literal
17Operationoperator: 20
operands: 21
18Literal
19Variable
20Literal
21ExprTuple22, 23, 24, 25
22Literal
23Literal
24Literal
25Variable