Expression of type Mult

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 Variable
from proveit.linear_algebra import Norm
from proveit.numbers import Abs, Exp, Mult, Neg, e, i, pi, two
from proveit.physics.quantum import ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
expr = Mult(Abs(Exp(e, Mult(two, pi, i, Exp(two, Neg(Variable("_a", latex_format = r"{_{-}a}"))), _phase))), Norm(ket1))

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())

\left|\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-{_{-}a}} \cdot \varphi}\right| \cdot \left \|\lvert 1 \rangle\right \|

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 16 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 4 operand: 8
3	Operation	operator: 6 operand: 9
4	Literal
5	ExprTuple	8
6	Literal
7	ExprTuple	9
8	Operation	operator: 22 operands: 10
9	Operation	operator: 11 operand: 15
10	ExprTuple	13, 14
11	Literal
12	ExprTuple	15
13	Literal
14	Operation	operator: 16 operands: 17
15	Literal
16	Literal
17	ExprTuple	24, 18, 19, 20, 21
18	Literal
19	Literal
20	Operation	operator: 22 operands: 23
21	Literal
22	Literal
23	ExprTuple	24, 25
24	Literal
25	Operation	operator: 26 operand: 28
26	Literal
27	ExprTuple	28
28	Variable