Expression of type Exp

from the theory of proveit.physics.quantum.QPE

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 k
from proveit.numbers import Add, Exp, Mult, e, i, pi, two
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = Exp(e, Add(Mult(two, pi, i, _phase, k), Mult(two, pi, i, _phase, two_pow_t)))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\mathsf{e}^{\left(2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k\right) + \left(2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}\right)}

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 16 operands: 1
1	ExprTuple	2, 3
2	Literal
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 9 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	18, 12, 13, 14, 11
9	Literal
10	ExprTuple	18, 12, 13, 14, 15
11	Variable
12	Literal
13	Literal
14	Literal
15	Operation	operator: 16 operands: 17
16	Literal
17	ExprTuple	18, 19
18	Literal
19	Variable