# from the theory of proveit.physics.quantum.QPE¶

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 e
from proveit.numbers import Add, Exp, Mult, Neg, frac, one, subtract, two
from proveit.physics.quantum.QPE import _two_pow__t_minus_one, _two_pow_t

In [2]:
# build up the expression from sub-expressions
expr = Add(subtract(Mult(frac(one, Exp(two, one)), _two_pow_t), two), Add(Neg(_two_pow__t_minus_one), one, Neg(e)))

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(\left(\frac{1}{2^{1}} \cdot 2^{t}\right) - 2\right) + \left(-2^{t - 1} + 1 - e\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(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')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 27
operands: 1
1ExprTuple2, 3
2Operationoperator: 27
operands: 4
3Operationoperator: 27
operands: 5
4ExprTuple6, 7
5ExprTuple8, 34, 9
6Operationoperator: 10
operands: 11
7Operationoperator: 32
operand: 29
8Operationoperator: 32
operand: 17
9Operationoperator: 32
operand: 18
10Literal
11ExprTuple15, 16
12ExprTuple29
13ExprTuple17
14ExprTuple18
15Operationoperator: 19
operands: 20
16Operationoperator: 25
operands: 21
17Operationoperator: 25
operands: 22
18Variable
19Literal
20ExprTuple34, 23
21ExprTuple29, 30
22ExprTuple29, 24
23Operationoperator: 25
operands: 26
24Operationoperator: 27
operands: 28
25Literal
26ExprTuple29, 34
27Literal
28ExprTuple30, 31
29Literal
30Literal
31Operationoperator: 32
operand: 34
32Literal
33ExprTuple34
34Literal